FREEWAY LEVEL OF SERVICE AS INFLUENCED BY

VOLUME AND CAPACITY CHARACTERISTICS

by

Donald R ,, Drew Ass1stant Research Engineer

and

Charles J. Keese Executive OfHcer

Research Report Number 24-3

Freeway Surve1llonce and Contrcl Research Project Number 2-8-61-24

Sponsored by

The Texas Highway Department In Cooperat!on wlth the

U, S, Department of Commerce, Bureau of Public Roads

January 1965

TEXAS TRANSPORTATION INSTITUTE Texas A&M Un]verslty College Station, Texas

ACKNOWLEDGEMENTS.

This paper is a summary of several years of research conducted by many researchers in the Texas Transportation Institute. We acknowledge the studies and unpublished work of the following individuals which have been incorporated in this paper:

Ginn, J. Royce, 11 Peaking Characteristics on Urban Freeways 11

Haynes 8 J 0 J 0 r 11 Freeway Level of Service as Influenced by

Peaking and Lane Use Characteristics 11

Jones u Dennis W., 11 Lights-On Study 11

Lipscomb 1 John, 11 The Effect of Ramps on the Lateral Distri­butlon of Vehl.cles on a Six-Lane Freeway".

Sincere appreciation is expressed to Dr. Charles Pinnell, Supervisor of the Gulf Freeway Surveillance Project, for his inspiration concerning the theoretical approaches to capacity characteristics, and his cooperation in devoting one phase of the project research to the testing and applicaUon of these theories.

Gratitude is also expressed to the Highway Capacity Committee of the Highway Research Board 8 and to many of the individual members whose ideas are included in this report.

ii

TABLE OF CONTENTS

Introduction

The Problem

The Approach

Volume Characteristics

Peaking Characteristics

Lane Distribution Characteristics

Capacity Characteristics

Theoretical Approach to the Capacity-Level of Service Concept

Measurements and Relationships

Applications

Freeway Design

Freeway Operations

Summary

Appendix

iii

1

1

3

4

4

8

22

22

31

49

49

59

66

69

The Problem

11 Level of Service,,'* as appHed to the traffic operat:on on a part:.­cular roadway a refers· to the quality of the drivi.ng conditl.ons afforded a motorl.st by a partjcular facillty o Factors which are mvolved ~n the level of serv:J.ce are; ( l) speed and travel time 1 (2) traffic interruptlon 1

(3) freedom to maneuver". (4) safety J (5! dr1.vlng comfort and convenience, and {6) vehicular operational costs c • ~

Each of the foregoing factors ls somewhat rela+ed tc all the others 0

The volume of trafflc using a fac:l:ity affects all of the factors and, i.n general, the greater the volu.rne .. the more adverse are the effects, As the raHo of the vol-ume of traff1c on a facihty to the volume of trafflc the facE­.ity can accommodate approaches umty, congestion ir.creases, Congest:on j s a quaL::.taHve terrr. _ long used by the general public as well as trafhc englneers ,. wh1ch refers to what can quant:>tatlvely be defined as vehicular denslty ., The end result of an over supply of veh~cles 1s the formation of a queue of stopped (or "crawllng" J vehicles at bottleneck locahons (a libreakdown'· of the operat1on,' such that volumes momenta:n~y drop to zero. leavmg only congest1on on the facilHy unt1l a clearoui: can be eftected

Traff1c vclumes are known to be con~muously vanable: even at very low hourly volumes there will be 1nfrequent _. short-term occasjons when a relat1vely large number of vehjcles w11l pass a given poj::.t. There also are reg1ons en a facn~ty wh1ch due to the georne1:ry, :nherently Wi.ll tend to accommodate fewer veh1cles, Th.ls :mpl:es that bottlerecl< s do ex:st and thus the level of service on a g:ver fac~l~ty may vary even w1th a 'ccnstan1:'' hourly volume !3ottlenecks may be f~xed in space due to the aforementioned geometrical cons1dera.twns of the facj]Jty and thus may be studied at the particular locat:on Such geometncal aspects as entrance and ex:t ramps have been stud:ted and evaluated as bottlenecks :t 1s pcsslble also_ how­ever- that the random "bunchmg" of veh1cles at any po:nt :n space may result m ''bottleneckil"'g'! due to the stat:st1cally va-~ab!e natt.,re o! streams of veh:cles, m wh1ch case_ the designers shccdd be able to pred~ct such peaking characteristjcs ln order to assure acceptable leveis o: ser~r::.ce,

BasiCally .. congest10n wlll be the dtrect result of the natti.re of the "supply and demand" on a facHity- The supply_, }Tl terms of traf:;:c eng:neer-1ng; has been referred to as capacity; the demand placed on the facility is j

as it implles, the number of motcrlsts who would seek to use the facHity,

and can be estimated by origin and destination surveys if the times of the desired trips are obtained. It is often futile to measure the flow of traffic on an existing facility with the objective of determining the demand on that facility. About the only relationship between existing volumes and actual demand which can be determined from such measurements is whether the demand is 1 in fact 1 as large as the capacity during any significant length of time during a day. In borderline instances, peaking occurring within a peak hour might show where capacity is exceeded by demand for intervals of time less than one hour. Even this feature can not be exhibited by a traffic system which is so inadequate that it limits (or "meters") the input of vehicles such that the volumes are less than the capacity of the particu­lar facility being studied.

If it is possible, in a given system, for more vehicles to enter than the facility can handle, then congestion will result whenever the demand exceeds capacity and the accompanying inefficiency results in fewer numbers of vehicles being accommodated by the facility in a given period of time. It is theoretically true that there is some maximum number of vehicles which can use a facilityl. This "possible capacity" is the vol­ume of traffic during the peak rate of flow that can not be exceeded without changing one or more of the conditions that prevail. From this value more restrictive conditions of roadway and traffic conditions are imposed to describe the measure of "level of service" that a given lane or roadway should provide. If the conditions are associated with highways or streets to be constructed at a future date, it is defined as design level of service. If the conditions express prevailing traffic flow conditions, it is designated as operational level of service.

Various volume levels can cause various levels of operating conditions, or levels of service. For any volume of vehicles using a particular facility, there is an associated level of service afforded these vehicles. It is pos­sible that the input of vehicles into a particular facility will be regulated such that traffic volumes will not exceed a predetermined, suitable level of service volume. Such operational control procedures are being investigated and seem to offer considerable promise.

Altho.ugh the use of a design level of service volume has considerable appeal in that it conforms to traditional engineering practice, the deter­mination of such a volume, relative to various. levels of service, is complex. There are regions on a freeway which are subject to more restrictive vehicu-· lar operation, such as in the vfcinity of an entrance ramp or exit ramp. Such regions should be. considered when determining the design volume of a facil­ity and a knowledge of the operational characteristics and traffic requirements

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at such locations is necessary for proper planning in order to avoid future bottlenecks o

The Approach

This report deals with two main topics which affect traffic operation, and thus the level of service 9 on freeways o They are volume characteris­tics and capacity characteristics o The capacity of a highway facility is a measure of its ability to accommodate vehicular traffic 0 Thls abHity depends, not only on the physical features of the road itself_, but also on the traffic demand and the interacUon. of vehicles in the traffic stream. The traffic demand on a highway facility is ex pres sed in terms of volume o

It should be apparent then$ that an appreci.ation of freeway volume character­istics is important in the planning, design and operation of freeway facilities,

Freeway volume characteristics utilize some of the same parameters defined in the more general subject of volume characteristics, First 1 the maximum observed volumes on different types of highway facilities, not only provide an indication of the magnitude of traffic demand 1 but establish a lower limit of possible highway capacity o The variations in volume for different time periods are explored for the1.r effect in the selection of representat1ve design hourly volumes o These cyclic patterns incjude monthly; daily, hourly and peak period vartaUons o The distribution of veMcles by direction and lane and the composH~.on of traffic are important design consideratwns; whereas the longitudinal dtstribut10n of vehicles has con­siderable practical signlf]cance as our emphasis gradually sh]!ts from free­way design to freeway operations and controL

Two ma1n topics under volume characteristics are considered and developed, The first 1 s an analysis of such peak flow characteristl.cs as peak rates of flow; correlation wi.th various parameters} and a com­pari son of peak two-hour volumes wlth peak one-hour volumes o The second main top1c under volume characteristics deals wlth studies of lane distribution of vehicles on freeways wHh partlcular attention given to the effect of entering and exiting vehicles on the lane use distributions o

"-- The second sect10n deals with freeway capaclty characterisUcs, including a theoretical approach to providing a rational relationship between capacity and level of service, It is significant that the first section deals with freeway demand and the second with capacity, In the third secti.on, applications are made of these demand and capacHy characteristJcs to free­way desi.gn and operations,

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VOLUME CHARACTER~STlCS

Peaking Characteristics

The need to consider the peak rates of flow wi!hm t.he peak hour has been recognized for several years z .. 3, 4 o5 and has been given con­siderable attention by the Capacity Committee of the H.:ghway Research Board.

No matter what criteria are used for the des;.gr. and operat~on cf a freeway 1 it is necessary to know what the trafflc demand w:ll be. Al­though no definite Hmlts have been establlshed as yet for the factors affecting the level of service, there will have to be some correlaUor:. betweer. _peak volume and level of servi.ce. An origi.n-desi;i.na!!.cn survey whi.ch denoted, to the nearest five minuteso when mctonsts wodd desjre to begin their tr:ps, could y~.eld valuable informati.on abcut the :rue rcature of the existing demand on an urban transportation system. The peak demand periods, however 1 would likely exceed the economical lim1ts of any system which could be provided. In some instances. depending upon the data available o reasonable estimates can be made of future peak hour volumes, A peak-hour volume does not 1 however, necessarHy irr..ply that a h~gh ra~e of flow wHl exist for less than a full hour a more than ar: hour, or apprcxi.­mately one hour; it ~s simply an ese.mate of the maxjrnum ncmber of vehicles expected or. a facil:ty during a full 60 minute per.>cd. Due to the natcre of the peak hour demand and the staEsUcally variable nature of traffic, :t is known that short term rates of flow wlthi.n the peak hour are often quHe variable.

The statistical variabiUty of volumes of traffJc is affected by the Ume period involved. As the time period is reduced, the average number of vehicles for that time period wUl reduce accordingly o for example, if the average hourly volume were 1800 vph, the average minute volume would be 30 vpm and the average second volume would be 1/2 vps. based on the hourly volume. The variability of smaller mean values is greater than that of larger mean values 1 when expressed as a percentage of the mean. The narrowing of the confidence interval band for increasing mean values is characteristi.c of not only the Poisson distribution, which closely approximates the distribution of light volumes of traffl.c, but also the many other distributions which have been used to approximate various actual traffic distributions. Even the normal distribuhon exhibHs these same characteristics although it is rarely used as an example of exl.sti.ng traffic distributions. Thus 1 even without the occurrerce of a change of

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volume within a given peak hour, a short term period within this hour has increased probability of exceeding its mean by a given percent than does the whole hour.

For planning purposes, future vol~mes are presently estimated for the peak hour or two hour period. In order to relate such volumes into a design peak rate of flow, the factors which affect this relationship must be established and evaluated.

Data from more than 200 freeway traffic studies were obtained from the Texas Highway Department, Bureau of Public Roads (Ramp Capacity Studies), previous studies conducted by the Texas Transportation Insti­tute and specific studies conducted on this project. The relationship between short-period traffic Uow (5-minute flow) to total hourly flow was determined from this data.

Because the 11 loading 11 of the freeway in some instances is controlled by the capacity and operation of the supporting street system and inade­quate capacity also sometimes limits 11 Unloading 11 which results in im­paired freeway operation, there was not sufficient knowledge of each of the freeways, except those in Texas and a few other specific sites, to permit consideration of these characteristics. It is possible that much better correlations of the results would have been possible had all con­ditions been known. Those freeways known to have good 11 loading 11 and "unloading .. characteristics showed very good correlation of the data.

Although many characteristics related to trip generation such as 9 eogra phi cal and time concentrations of trips, character of the freeway (radial, circumferential, etc.) character of supporting street system, population, area served, and others perhaps have marked effects on the peaking characteristics 1 it was possible from the data available to study only the relationship of peaking to the population of the city or urban area. The results are shown in Figure 1. These curves are based on the data for 132 peak periods from studies in 31 cities in 18 states. Congestion was not apparent in the immediate vicinity of any of the study sites. The variables are statistically significant and the curves fit the available data with a standard deviation of 5%.

Figure 2 shows the relationship between estimated rates of flow and .. .)bserved rates of flow and includes a 10% error band within which most points were included. Figure 3 shows the frequency distribution of the percent error involved in using Figure 1 to estimate the peak rates of flow. As can be noted I the errors are somewhat normally distributed.

-5-

if >

v /

v 1/ /

/ l/

EXAMPLE I

Population of Metropolitan Area

11 1,000,000

Assigned Volume =5,000 VPH

Design for 5900 VPH

as Peak Rate of Flow

1-+--+-++-H-H-+HI--+--1-+-1~+-+-++l--l---~-+- ·H+ict+HI-t+H+t+tH+++IH+Hl-t+H+t+HI

. - - . 1-H-I-H+I-Ht-++++H-1+11

3000 4000 5000 6000 7000 8000 9000

PEAK HOUR VOLUME - VPH

DETERMINATION OF THE RATE OF FLOW FOR THE HIGHEST 5-MINUTE INTERVAL FROM THE RATE OF FLOW FOR THE WHOLE PEAK HOUR

FIGURE I

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I 'I I

0 -1000 --wo:: ~:::> ~~ -500 ~0:: w~ 0 Cl) C/)CI) ww ...Jd +500 ...!_ :3I t;~ +1000+ <i 0

J"i-= .... • .- . . -.- .. .. . . ·. . . . ......._ .. . . . . . .. . . . . :

• 1•.

. . :-•-­. . ., . . . • .·

+ t0°/o.

....... :. . • : ' . . • . . .

..

-10%

•

• •

ESTIMATED HIGHER THAN OBSERVED

ESTIMATED LOWER THAN OBSERVED

1000 2000 3000 4000 5000 6000 7000 8000 9000 OBSERVED RATE OF FLOW

THE RELATIONSHIP BETWEEN THE ERROR, IN VEHICLES PER HOUR, AND THE OBSERVED RATE OF FLOW

FIGURE 2

~NORMAL DISTRIBUTION I~

cr=

-18 -15 -12 -9 -6 -3 0 3 6 9 12 15 18 PERCENT

FREQUENCY DISTRIBUTION OF PERCENT DIFFERENCE BETWEEN ESTIMATED AND OBSERVED RATES OF FLOW

FIGURE 3

A series of multiple regressions were run on available data in an effort to determine the factors affecting the maximum rate of flow occur­ring in a peak hour, Consideration was given to the following items: the physical size of the metropolitan area, the concentration of the central business district, the distance of the study site from the main destination or generator (m general the central business district), the population of the metropolitan area as measure of the complexity of the traffic system, and the actual size of the peak period ltselC and whether the peak occurred in the morning or afternoon. A few of the cities with multiple study sHes indicated a definite relationship with the distance from the major generator e while others did not, It was disconcerting to note that this relationship was often contradictatory between studies o

In the light of such varying results, no relationship could be positively identified, The same was true of most of the other factors o

Improved traffic assignment methods e involving comprehensive programs utilizing large digital computers, are being used to develop predictions of urban traffic volumes for a peak two-hour period. ln order to establish a relationship between two-hour peak periods and one-hour peak periods, the data from the studies mentioned earlier were · analyzed, Figure 4 shows the results obtained from 9 5 studies for which two-hour peak volumes were available~ It can be noted that the peak hour volume can be expected to lie between 55 percent and 60 percent of the peak two-hour volume.

By using the relationships shown in Figure 4 and Figure 1 6 the design volume can be obtained from the peak two-hour volume. These design volumes will take into account the peaking effect"

Lane Distribution Characteristics

Critical sections on the freeway often exist adjacent to ramps and, i.f a certain level of service is to be assured. the motorists, it is neces­sary to give close consideration.' to puch.:ar,~~~, irr the d~s~gn of freeways. Because the merging problem directly iiwolv~s traffic in the outside ·lane and the entering ramp traffic 1 a study was m·ade of the percent of total freeway traffic using the outside lane 0 Only six lane freeways were con-. sidered in this particular project.

A three part research project was· made involving data obtained from. forty-nine study sites located on fourteen different six-lane freeways in ten different states. First, emperical relationships were developed which

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68 STUDIES IN TEXAS 27 STUDIES IN 14 OTHER STATES

6000

(j) 5000 w ...1 ~ :I:

~ 4000 -w :a:

I 3 3000 0 <.0 > I

a:: 5 2000 ::c

~ <! ~ 1000

ll I I I I f

! I j· l : -I I I I I T L .• : I : ' I I I T-1 T T . . ' I I . j_ '

I

i l I. i I l IT~ _ : 1 · : I 1 r A •1

I ' i I j_ - ' ! _....&..c"f..-! I I : . ! i I i · 1 .xJs·~~ «.lof<~" I ! T . ; ; ! • . i ' ; I ' I I ... - • ../1 I : ' . ' ' , ~··'Y' I •: ~~ . ' I i ' I . ~ T i/T-A I---<

1 1 1 · · I v-~, . v . 1 i . / • •

1

1 I I I : V-[ -· ' T-i I · "V/ I ' L' I . ' • I I l IT: i ~:?· ' I !

i I I I .;4) . I . : I I . ---<

~ I~ 11

'I I I : :::..-1 i . ' I ' I· ! -i

-' , ~I. · 1 '1, • I . . ' ' ' 'I ILl I i /"" ' i_ J ; I I i i ! I ---r:p- . rl I ' 1 I . l 1- .,.P"'I : I • I I I I I l i

I ""1 I T ' : i I : j I . I i I l 1-L-- liliiTJ: I i :1! • i i _j [ I i I i I I : 1

i I I J O 0 I 000 2000 3000 4000 5000 6000 7000 8000 9000 10000

TWO HOUR PEAK PERIOD VOLUME (VEHICLES)

DETERMINATION OF THE RATE OF FLOW FOR THE PEAK HOUR FROM THE RATE OF FLOW FOR A TWO- HOUR PERIOD

FIGURE 4

Jest fit the data of eight representative study sites. Parameters which Nere found to be significant were freeway volume, entrance ramp volume, J.pstream ramp volume, distance to upstream ramp, downstream exit ramp volume, and distance to downstream exit ramp. Second, the relation­ships which were developed were then used to test against all study sites for validity. The third step was the development of a design procedure which was used for practical applications. Figure 5 shows the relationship between the percent of the total freeway volume in the outside lane and two of the parameters - total freeway volume and entrance ramp volume. The mono­;Jraphs shown in Figure 6, Figure 7, and Figure 8 represent the relationships between the percent of the total traffic in the outside lane and the volume on, and distance to, an upstream exit ramp, the volume on, and distance to, a downstream exit ramp, and the volume on, and distance to, an upstream entrance ramp, respectively. Distances are referenced to the ramp nose, in each case. A downstream entrance ramp was considered to have no effect on the percent to traffic in the outside lane.

The predicted percent in the outside lane can have no less variability than the ordinary or natural variability of the data in general. The 90 percent confidence limits for each of the freeway and ramp volume groups were calculated and the following is a tabulation of such variability:

Freeway Volume (vph)

2000-3000

3000-4000

4000-5000

5000-6000

Natural Variability in the Percent in the Outside Lane

+ 8%

+ 5%

+ 3%

+ 2%

The "natural" variability of the data was arbitrarily defined as the range within the 90% confidence interval. The large natural variability at freeway volumes less .than 3 000 vph is not considered significant since this volume is well below the design volume used on six-lane freeways. A comparison of the observed percentages minus the predicated percent­ages in the outside lane was made for 1212 five minute volumes taken from the 49 study sites. Appendix A is a tabulation of these differences.

It is intended that the method presented here for six lane freeways be

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w 2 <t ...I

w 0 CJ)

I-

30

25

20

51 5

2

1-2 w u 0:: w a.

0

5

0 1000

ENTRlNCE RAMP VOLUME VPH

... ·· .. .,. -ooo

'2,.00---~ ~ ~

~ /

~ rooo v

- - -- - -

A

T7~1

PERCENT OF TOTAL FREEWAY

VOLUME AT ·~· FOR RAMP AND FREEWAY VOLUMES

2000 3000 4000 5000 6000 TOTAL FREEWAY VOLUME VPH

RELATIONSHIP BETWEEN THE PERCENT OF THE TOTAL FREEWAY VOLUME IN THE OUTSIDE LANE AND THE ENTRANCE RAMP VOLUME

FIGURE 5

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--.... -

7000

TOTAL FREEWAY VOLUME VPH

3 4 5 PERCENT SUBTRACTED AT ''/1.' DUE TO EXIT RAMP UPSTREAM AT "X"

.............,,...~'--'-'-~~-· · · · · · · · · · ········EXAMPLE: EXIT VOLUME ........... 600 VPH DISTANCE ................. 500 FT. FREEWAY VOLUME .. .4000 VPH ORIGINAL% ................. 22.5% CORRECTION % ............... 2 "'o CORRECTED % ............ 20.5%

-CORRECTION TO THE PERCENT IN LANE I DUE TO EXIT RAMP DOWNSTREAM

FIGURE 6

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TOTAL FREEWAY VOLUME VPH

PERCENT ADDED AT "A" DUE TO EXIT RAMP DOWNSTREAM AT X

·--------------A

7/ ......................... EXAMPLE I

·a~··· EXIT VOLUME ...................... 500 VPH DISTANCE .................................. 400 FT. FREEWAY VOLUME ............ 4000 VPH ORIGINAL % .......................... 2 7 % CORRECT ION ........................ 2.3% CORRECTED % ..................... 2 9.3 %

CORRECTION TO THE PERCENT IN LANE I DUE TO EXIT RAMP DOWNSTREAM

FIGURE 7

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TOTAL FREEWAY VOLUME VPH

/

~~~~L4~-~+-~~so~~v~

~~~~L4~~+--~oo~~~~~~ «;~~

~~~+-~~~30~~~~~0~ 200 -\)q,<? ..#

Q;-~

3 4 5 67 89 PERCENT ADDED AT A DUE TO ENTRANCE RAMP UPSTREAM AT "X"

··EXAMPLE: ENTRANCE VOLUME ......... 650 VPH DISTANCE .................... 600 FT. FREEWAY VOLUME ......... 3800 VPH ORIGINAL% ........................ 22% CORRECTION % ................... 1.8% . CORRECTED % ................... 2 4%

CORRECTION TO THE PERCENT IN LANE I DUE TO ENTRANCE. RAMP UPSTREAM

FIGURE 8

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extended to include four lane and eight lane freeways. In an effort to determine general relationships for four, six and eight lane freeways similar to those shown for only six lanes in Figure 8, data from 13 2 peak periods were analyzed. These data were the same as that used in peak­ing characteristics ·study and included over 2000 five minute volumes from 31 cities located in 18 states. Multiple regression techniques were used to develop equations from these data and Figure 9 shows the families of curves which were developed from the equations. A multiple correlation coefficient squared, R a 1 is generally understood to represent that portion of the variability, or variation, which is accounted for by the derived equations o The following is a tabulation of the obtained R :as o

Four Lane Freeways Multiple R square = 0. 51

Six Lane Freeways Multiple R square = 0. 70

Eight Lane Freeways - Multiple R square = 0. 48

It is interesting to note that, for the entire range of values shown in Figure 9, the standard deviation was approximately 200 vph. Expressed as a percentage, however, at lower outside lane volumes of 1000 vph, there would be a standard deviation of 20 percent.

It is known that factors other than freeway volume and ramp volume affect the percent of total freeway traffic in the outside lane. Further studies of tHose factors are; being mude so that norhographs similar to those shown in Figures 6 to 8 can be prepared,

As previously mentioned, there is an important relationship between trip length and outside lane utilization. Drivers entering the freeway for only relatively short trips could reasonably be expected to remain in the outside lane. In an attempt to evaluate such relationships, a single study was conducted on the North Central Expressway in Dallas using the 11 Lights-0n 11 study technique previously used by the New York State Department of Public Works and the Port of New York Authority6 .

Figure 10 shows a scheme of entrances. exits, and observati.on points along the two and one-half miles of the six-lane freeway study section. Vehicles entering at the Mockingbird entrance ramp were advised by signs to drive with their lights on for 20 minutes. Police­men were standing near the signs and would call motorists' attention to the message by simply pointing to the signs. Observers were located at strategic points along the freeway, generally on the cross-street over-

-15-

w z <t ...J

m a: ;:) (.)

~

w ~ ;:) ...J 0 >

r <t 3:: w w a: LL.

<!) z

I :X: (.) ....... <t en

I 0 a: a. a. <t LL. 0

1-z w (.)

a: w a.

50%~------------+----+----+----+----+----1----~--~~--~----~--~----+----+----+----4

FOUR LANE FREEWAYS

R=O

40%L-----~----+---~~~~~~--~~~~~----t---~---+--~~--t----r---t--~ = 400

= 600

:.~ ~ ' I ! SIX F~! ' I I I I ' ' I --+ I 1::::::1 I . I I . . ! .

30 ··I I I R •0 I I i : . = 200 '

I =400

=600 20% I ' j • -~---7---:-:--+---+--+----=-,..,::::::--!-----i

' I =800 ~ :.1000

i I

1 , : rl . 1 I i j l i EIGHT LANE FREEWAYS i ! i

10 o/, ' I . --- +-· I I i I I 0

i i i R=O TO R=IOOO 11 i f I' I 1 I R = Ramp Vol e ! . ~ ! . I I I i

! I I I I I I 0%~· __________ J_ __ ~---~--~----L---L--~L---~-~----~--~----~--~----~~

1000 2000 3000 4000 5000 6000 7000 8000

FREEWAY RATE OF FLOW APPROACHING ENTRANCE RAMP

RELATIONSHIP BETWEEN PERCENT OF TOTAL FREEWAY VOLUME IN THE OUTSIDE LANE AND FREEWAY AND

RAMP VOLUMES FIGURE 9

(10) OFF RAMP

(9) HASKELL

(8) OFF RAMP

ON RAMP {II) VOLUME COUNT AT FITZHUGH '"lr-:-:-o--(7) FITZHUGH

(4 MEN) (6) OFF RAMP

NOTE:

ON RAMP '-rr-r-1,..,.---{5) KNOX- HENDERSON

(4) OFF RAMP

ONE MAN AT ALL OFF RAMPS ON RAMP

FOUR MEN AT ALL OVERPASSES ...,_,._,--r--_(3) MONTICELLO

(12) ON RAMP AT MOCKINGBIRD (2 MEN)

(13) VOLUME COUNT AT MOCKINGBIRD (4 MEN)

ON RAMP ~'-'--(2) Me COMMAS

(I) OFF RAMP

RAILROAD {M.K.a T.)

ON RAMP

MOCKINGBIRD

STRIP MAP FOR OBSERVATION LOCATIONS

FIGURE 10

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pass structures and at each off-ramp,

As the vehicle entered the freeway 1 the last four dig:ts of the license number and the vehicle type were recorded.. Failure to turn on headlights was noted in order to determine compHance ratios,

As the vehicle with headlights on moved through the study area 9

the observer at each point would record the license number" vehicle type and the lane in which the vehicle was travelling, Observers located at each exit ramp recorded the license number of each vehicle with headlights on, Each observer noted the end of each 5-minute period on the data sheet,

Freeway volumes were counted, by lanes~ at two locations during the entire study period of four hours, One volume count station was located at the beginning of the study section and one at the end of the section. Volumes were recorded in 5-mi.nute intervals,

During the four hour study period over 1800 vehicles entered on the Mockingbird ramp and over 1500 complied by turning on thel.r headlights o About 1100 of the complying vehicles did not exit wHhin the study area and about 400 vehicles were noted to exH at on.e of the five ex1t p01nts wHhin the study section.

Regarding the study method, the following can be summar1zed o

1 o The 11 lights-on11 study method was an effectlve means of studying the lane use related to trip length on this particu-­lar freeway which had numerous major street overpasses,

2, The presence of the signs, policemen, or observers had no noticeable effect on the traffic flow,

3, Compliance raUos in the 7 5-8 5 percent range were obtained by using this method, The sample si.ze was much higher and less expensive to obtain than by other methods consi.dered o

4 o Proper desi.gn and location of signs is a big factor in obtain­ing high compliance ratios,

5o A loud speaker was not essential o

6 o A policeman can be used to advantage to encourage motori.sts

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to observe the signs.

7. Newspaper, radio, and television publicity can be. beneficial, but is not necessary for adequate compliance ratios.

Figure 11 depicts three-dimensionally how the vehicles entering at the Mockingbird ramp were distributed over the three lanes as they travelled toward the Central Business District. The dark portion at the bottom of the outside lane represents that portion of those entering vehicles which exited within the study area. A large percentage of all such exiting vehicles used only the outside lane and, as a result, those vehicles can not be noticed in the two inside lanes.

The t9tal v9lume of traffic on the freeway has an effect on the lane usage of entering traffic. As the total volume increases, entering vehicles are more restricted to the outside lane and motorists view a temporary lane change less worthwhile in view of the fact that another lane-change opportunity must be found to return to the outside lane prior to exiting. Figure 12 shows the relationship between trip length and the percent of the entering traffic in the outside lane. The uprer portion of Figure 12 ·pertains to only light total freeway traffic volumes of less than 3000 vehicles per hour, one way. The lower portion of Figure 12 corresponds to conditions of moderate to heavy total freeway traffic volumes of over 3 000 vehicles per hour, one way. Although ·the observation points are widely spaced, it would seem that the restrictive effect of the higher volumes is noticeable.

Figure 12 indicates that "ordinary" or 11 equitable" lane use dis­tribution is only attained by those vehicles travelling several miles on the freeway. Those vehicles travelling less than three miles can not be expected to reach thcit "steady-state .. lane distribution which is characteristic of .. through .. vehicles.

It must be pointed out that this is the result of a single study. It is expected that this study will provide a basis for further work of a similar nature.

-19-

I N 0 I

t~t~o'~~ ~ ..,P.~ y

o"'t(. .,~ ~\O~t(, ~ .._P'

~

of(.~

s"'o~~~t(.

~r ...... .,,,~~:,,, / Jr,l" .. 'e-. c.~ ~ s :'\~!>-~ Jr,l" o, ·.?%

0 ~~ \ ~'1

\

!!::

e-. , ..r,l" ,

<(~0~ ~ ~

_,(j~ e-~ ~, :'\!>-', \ "'l"

Q\'?:1 0 , %

'

o <I.e

e- o,

\

..r,l" I.e , %

FIGURE II

<~., % LANE USE DISTRIBUTION ·

BY VEHICLES ENTERING AT MOCKINGBIRD RAMP

DISTRIBUTION BY PERCENT IN EACH LANE

1444 VEHICLES IN SAMPLE

100

90

lLI z 80 <(

-' 70

tJJ 0 60 u; 1-::> 50 0

~ 40

1- 30 z lLI 0 20 0:: lLI 0.

10

0 0

100

90

lLI z 80 <(

-' 70

lLI 0 (/) 60 1-::> 50 0

z 40

1- 30 z 11.1 0

20 0:: 11.1 0.

10

0 0

EXIT NO. (4) (6) (8) (10)

TOTAL FREEWAY VOLUME LESS THAN 3000 VPH.

2000 4000 6000 8000 10,000 12,000

DISTANCE FROM ENTRY POINT

EXIT NO. (4)

TOTAL FREEWAY VOLUME MORE THAN 3000 VPH.

2000 4000 6000

(6) (8)

10

VEHICLES NOT EXITING

WITHIN STUDY AREA

0

8000 10,000

DISTANCE FROM ENTRY POINT

(10)

0

OUTSIDE LANE USE RELATION WITH TRIP LENGTHS

FIGURE 12

-21-

12,000

CAPACITI:' CHARACTERlST!CS

Theoretical Approach to the CapacHy-Level of Service Concept,

Both capacity and level of service are functions of the physical features of the highway facility and the ~nteract~on of vehicles in the traffic stream, The distlnctwn is this~ A given lane or roadway may provide a wide range of levels of service, but only one possible capa-city, The various levels for any spec1flc roadway are a function of the volume and composition of traff1c, A given lane or roadway desjgned for a given level of serv1ce as a specif1ed volume will operate at many different levels of service as the flow varies during an hour, and as the volume varies dunng different hours of the day, days of the week, periods of the year, and during different years with trafflc growth, In othar words fluctuations in demand do not cause fluctuations in c:1pacity. but do effect changes in the qualHy of operation afforded the motorist. In a very general way then highway planning, design and operational problems become a case of whether a certain roadway (capacity) can handle the projected or measured demand (volume) at an acceptable level of servi.ce (speed, etc,), Because of both observed and theoretical speed-volume relationships on freeway facilities c which shall be considered later_. it is poss~ble to anticipate to some degree just what level of serv.1ce can be expected for a given demand-capacHy ratio o The obvious weakness Ues m the fact that most of the qualltative factors affecting level of serv~ce can not be related directly to traffic volume" ·

Greater dependency on motor vehicle transportation has brought about a need for greater efficiency in traffic facllities o The motorist is no longer sati.sfied to be "out of the mud, 11 In facts fewer and fewer folks remember the days of unpaved roads o The freeway is an outgrowth of the demand for highways providing higher levels of service o The place that motor vehicle transportation plays in our society demands dependable service be provided by traffi.c facilities and the popularity or attractl.on to the freeway illustrates this point 0 It is very important that the engineer clearly under­stands the factors affecting efflc1ency or level of service of our highways and streets o

The indivl.dual·motorist seldom understands or appreciates efficiency of a facility in terms of volume accommodated" He evaluates efficiency in terms of his tnp - the service to hlm" He evaluates the operating con­ditions of speed 1 travel time u traffic interruptions s freedom to maneuver o

safety, drivi.ng comfort and convenience u operating costs a etc o The level

-22-

of service is a term which denotes the different operating conditions that occur on a given lane or roadway when accommodating various traffic volumes.

Recent contributions 7 to traffic flow theory regard traffic as a one­dimensional compressible fluid with a concentration, k, and a fluid velocity, u. The conservation of vehicles is explained by the following equation of continuity:

+ Q (ku) QX

= 0

If it is assumed that drivers adjust their speed in accordance with the traffic condition~ about them as expressed by the general expression kn ok/o x, the acceleration of the traffic stream becomes,

du dt =

Solving equations ( 1) and (2) for u=f(k), and making use of q=ku yields the following generalized equation of state for a traffic stream,

where uf is the free speed and kj is the jam concentration. The ex­ponent, n, provides some flexib1lity in fitting a theoretical flow concentration curve to a particular highwayS.

(1)

(2)

(3)

The speed of waves carrying continuous changes of flow through the stream of vehicles is given by the derivative of the q-k equation defined in (3),

1 - (n+3) 2

(n+ 1)/2 , n > -1

The concentration, km, at which flow is a maximum is obtained by setting ( 4) equal to zero and solving for k:

-2/(n+ l) km = [(n+3)/2] kj n > -1

-23-

( 4)

(5)

Repeating for dq/du = 0 gives the speed, urn, at which flow is a maximum,

urn= [(n+1)/(n+3)] uf, n>-1

It therefore follows that the maximum traffic flow obtainable on a roadbed (capacity) is

(6}

(7)

It has been hypothesized9 that discontinuities in traffic flow are propagated in a manner similar to 11 shock waves" in the theory of com­pressible fluids. The speed of a shock wave, U, is given by the slope of the chord joining the two points of the flow-concentration curve which represent the conditions ahead of and behind the shock wave,

u = (q - q ) I (k - k ) o a 1 a 1

Application of the mean value theorem suggests that the speed of the shock wave is approximately the mean of the speeds of the waves run­ning into it from either side,

u = 1/2 (q' + q• ) 1 2

where q~4 is given in equation (4). l,

(8)

(9)

The very strong analogy between traffic flow and fluid flow suggests that the conditions of continuity of momentum and energy should be ful­filled at the surface of a traffic shock wave, just as the equations of dynamic compatibility must be fulfilled in fluid dynamics o Multiplying equation ( 1) by u and equation (2) by k, then adding the two equations, we obtain

_Qjku) = at

o (ku 2 + kn+2 c a\ n+i}

ox ( 1 0)

Equation (10) is the law of conservation of momentum in the differential form as applied to traffic flow o Comparing equations (1) and (10) with the classkal forms i.n hydrodynamics 1 we can complete the analogy between the fluid and traffi.c quantitites 0 This correspondence is illus­trated in Table 1 o

Kinetic energy 1 ku 2 6 is the energy of motion of the traffic stream.

The measure of the jerkiness of the driving in thi.s stream is given by the standard deviation of the acceleration or acceleration noise, a .

-24-

I N CJ1 I

Variables

Parameters

TABLE 1

CORRESPONDENCE BETWEEN PHYSICAL SYSTEMS

Hydrodynamic System

Mass Density, p

Velocity, v

Momentum, pv

Shock wave velocity, U

Kinetic energy, pv2 /2

Internal energy, f:

Traffic System

Concentration, k

Speed, u

Flow, ku

Shock wave velocity, U

Kinetic energy, ku2 /2

Acceleration noise, a

The units of both parameters are those of acceleration, Energy, as expressed in these two quantities! is consistent with the level of service concept previously defined. Thus, the kinetic energy of the stream fulfills the fjrst level of service factor (speed and travel time) whereas ]nternal energy (acceleration noise) measures such level of servlce factors as traffic interruption and freedom to maneuver, and to some degree safety, comfort and operation costs.

Utilizing energy, rather than momentum, as the criteria for opti­mization depends on finding those values of k and u that ma~i.mize the kinet1c energy of the traffic stream, E, and minimize the i.nternal energy or lost energy) a- . Division of (3) by k, squaring the term and then multi plying by k yields

[ (n+ 1)/2 (n+1~ E = ku/ L -2~) · +~ J , n > -1.

Setting dE/ dk - dE/ du = 0 to get the appropriate "energy" parameters gives

-2/(n+ 1) k' =-(n+2) k. , n~-1,

m J

u~m = [(n-+1)/(n .... z)] uf , n > -1,

and

q' =k1"u' m m m

Dividlng equations (5), (6), and (7) by equations (12), (13} u and (14) respectively J we get

and

[2(n+2)] (n-3)

n-+-2 n~3

2/(n+ 1) , n > -1;

n > -1 ;

-26-

(11)

( 12)

( 13)

( 14)

( 15)

( 16)

2 2/<n+l)

J.n+2l (n+3'l

(n .. 3)/(n*' 1) n > -1

It is apparent that k 6 m < km and uG m >urn which 1 from the point of view of the motorist 1 suggests that energy is a better criteria for defimng opti.mum operatlon, Of course 1 thl.s ls accomphshed by a sacrihce in traffic flow 1 since qc m < qm"

Traffic engineers have long been faced with the d1lemma of relabng possible capacity to level of servJCe quantHatlvely. Much of the dlffi­culty can be attributed to the fact that capaclty is expressed in the umts

(17)

of vol uroe; whereas the term level of service is highly subjectlve in nature, Volume is a logical measure of efficiency from the point of view of the englneer 1 whereas motwn in the form of speed and the magmtude and fre­quency of speed changes is an important measure of level of ser':ice from the point of view of the individual driver"

The momentum-kineuc energy analogy seems to apply" 1f a moving mass strikes a statlonary object wlthout rebounding, as when the descend­ing block of a pile driver strJkes the p1le 1 the resultlng motwn of the la'f:ter depends on the momentum of the block and not upon lts JcneUc energy, Therefore: H a fixed amount of energy 1 s ava1lable. 1t 1s more effective to use a heavy mass movmg at a relatively low speed than a Hghter mass moving at a high speed~ The momentum of the slow-moving heavy mass after falHng a short distance is greater than that of a small rapidly movmg mass which has be.en llfted higher by the expenditure of the same amount of energy 0

Replacing mass 1n the prev•ous d1scuss1on with trafhc dertsHy. H 1 s seen that efforts to measure effidency in terms of momentum (traffic 11 throughput" l must necessarily be achieved with a high traffic stream denslty and a low traffic stream speed~ This is obviously not cor..sistent with the level of service concepL On the other hand. since energy is a scalar qli.antlty. the energy of a system such as a traff1c stream is equal to the sum of the energ1es of its constituent particles; and w111 be a maximum when 1nternal frlctlon caused by vehicular interaction .is a min~mum, Since this internal friction reflects some comprom1se on the individual driver's freedom to maneuver, his comfort. and h1 s safety 1

the energy concept Jnc1udes most of the qualitative ingredients defined in level of service, Moreover .• the energy concept affords the engineer the opportunity to treat level of service quantitatively,

If equations (3) and (llJ are expressed in terms of speed only j and

-27-

then normalized, they become (for the special case of n=1)

_g_ = 4 ~~f) -c~f7 J qm

and

~ = 4 ~~fJ 2

- c~f] 3 J qmuf

The curves of equations (18) and (19) are plotted in Figure 13, The right side of the graph is the well known volume- speed relationship normalized so that the abscissa is the ratio of flow to capacity and the ordinate the ratio of speed to free speed, Since division of the abscissa by the ordinate,

it is apparent that the slope of any ray is one-fourth the normalized traffic density, The optimum density rays, using both the momentum and energy criteria, are plotted.

The left side of the graph shows the relationship between the kinetic energy and speed of the traffic stream, Division of the abscissa by the ordinate,

=

gives the flow-capacity ratio. Thus, the maximum abscissa gives maximum kinetic energy (located at u 1 m=2/3 uf) 3 while the maximum slope gives the maximum momentum or flow (located at urn = 1/2 uf) o

The relationship between cap_acity and level of service is so fundamental to such practical aspects of traffic engineering as planning a

design and operations, it is important that the distinction between these terms be appreciated, This can best be accomplished by a quantitative relationship, based on the energy-momentum analogy, as expressed in the following definitions:

-28-

(18)

( 19)

(20)

(21)

... :ol=>

0 w w c.. (j)

0 w !:::! I ...J

N <t (.0 ::E I 0::::

0 z

SAFETY FACTOR , OR UNUSED CAPACITY AT OPTIMUM LEVEL

0.8

I

II

/I I I

I I I I

I

<S' SERV•CE •.Hq~

I

I I I

OPT SPEED (u,=2/3u1J BASED ON MAXIMIZING "KINETIC 1 ENERGY" OF TRAFFIC STREAM ------------------------------------------r----------------------------' . I I I ..-/1

I '' I : INCREASE IN LEVEL OF SERVICE ; _,. I I \ I 1 BY USING OPT. SERVICE VOLUME // I

N '- 0.6 / : INSTEAD OF POSSIBLE CAPACITY .... ..- I :;: ' I 1 2/3urll2u1 = l/6u1 .... 1 0 ', 1 / I ~ I '· I /

1 ', OPT SPEED (um=1/2u1 ) BASED ON MAXIMIZING '"MOMENTUM" 10F TRAFFIC STREAM ,/ I . --~-----------------------------~------~-------------~----------L--W-1 ,~ I I I / I -'~/ I ,<'0 I I _,._... /~ 1 '~ I I _,.. ~, ~ I

'r:. I I // ...-..-! ~ I -~'% I _,....- ,,...- I ::> 1

!a: ow! "- ::;:1 <t :::>I a: 61 ~>I cr 1 u wr "'~I <t a: I

WI i'; "'I

,5 ::;;1

01, 0.4 I I / ___ ..... I I ~ ''o 1 .... " I (o'-" ,.6' 1 I _,/ .--" I I ~ ""'-, ,~ I -' ,...,.,... I

r:.'~ I I // ..... --- I 9- :-. I .:'\ _,.. .-- I I 9 _,-+-v ...-" I ">.!,, , I • ,1_,.- ,...- ':g ~>-I

/0 ' I I ~/I ------ ::>1 :;: t- I , / \. ...- .-- ...11 ° u I

' 'c-J ,0--:_,.. : ,1'!. ~)..\..- ~I 0: if I '' 0 2 0 I ~"'-' / ~ ...-,.. I · - <t I

' . -\:I <J/ .- :"! 1,.~ t;'l ::!: u I ' I ;;-1 0«)/ ~c:.?.--'1 · >1 -~ I

~I / <:;)«.:....- I 0:1 z w I I .-_, o'<'~""' I l:it ~~I

I / /,_. I o"' I .-/ ...-' ~I ::!: :g 11

' :::>1 I ~~~~ .···r-INTERNAL FRICTION

I ~ h--..--L~ AT POSSIBLE CAPACITY I /_, ,' ::!:1 . a.. I / ...- i=l X I

1 .... _:/' ~! ~ !;{~. ;~ B1 I '::!: I 1 L_j__----1

0.6 0.4 0.2 0.0

NORMALIZED "ENERGY" (qu)/(qrJ11)

QUANTITATIVE APPROACH RELATIONSHIP USING

0.2 0.4 0.6 0.8

NORMALQED '~OMENTUMn FLOW I CAPACITY (q/qm)

TO THE LEVEL OF SERVICE -CAPACITY THE ENERGY-MOMENTUM ANALOGY

FIGURE 13

1.0

... =>I::J

0 w w c.. (j)

0 w N ...J <t ::E 0::: 0 z

Possible capacity is the maximum number of vehicles that can be handled by a particular roadway component under prevailing conditions. It is that product of the density and speed that maximizes the momentum of the traffic stream.

Level of Service refers to the quality of driving conditions afforded a motorist by a particular facility as reflected by (l) speed and travel time (2) traffic interruption (3) freedom to -maneuver ( 4) safety (5) driving comfort and convenience and (6) vehicular operating costs. Seven levels of service are described. (See Figure 13).

Level of Service A describes a free flow accompanied by low volumes I low densities, and high speeds which are controlled by the driver desires and physical roadway conditions (free speed). Although I the variance in speeds is high 1 there is no restriction in maneuverability due to the presence of other vehicles 1 and drivers can maintain their desired speeds with little or no delay. This is the service expected in rural locations.

Level of Service B 1 C 1 and D describe the zone of stable floW. The upper limit is set by the zone of free flow 1 whereas the lower limit is defined by the optimum density 1 k 1 m 1 and optimum speed 1

u 1 m 1 based on maximizing the kinetic energy of the traffic stream. 'The conditions at U

1 m and k 1 m are acceptable for urban design practice. The divisions associated between levels B-C and C-D are arbitrary.

Level of Service E · & E describe the zones of unstable flow. Zone E is set betweeri" the 6ptimum conditions described by the energ/ and momentum criteria. In this zone 1 small increase in volume is accompanied by both a large decrease in speed and ki­netic energy leading to high densities and internal friction which contribute to instability. Zone E is described by operating speeds lower than Urn and a traffic density greater than km, yet with a vehicular flow greater that q 1 m. This type of operation can not persist and leads inevitably to congestion.

Level of Service F describes a forced flow condition at low speeds and very high internal friction. Volumes are below capacity and storage areas consisting of queues of vehicles form. Normal operation is not achieved until the storage queue is dissipated.

-30-

Measurements and Relationshi_2s

The primary characteristics of traffic movement are concerned with speed, density and volume, These three fundamental characteristics are dependent on the geometric design of the roadway and the operati.onal requirements of the traffic stream, Interest in these charact.eristJcs is manifest in the need for establishing representative possible and practical capacities for freeway sections,

While any set of speed observations may be influenced by such items as demand, capacity 1 design, weather and controls, it is not generally appreciated that the location at which measurements are made has a great deal to do with the adequate description of operating conditions. For example, traffic data taken just beyond an entrance ramp may reflect smooth and uniform operation when actually the traffjc behind the ramp may be operating under stop-and-go conditions, Because congestion at one point may cause congestion for a great distance back along the free­way; a survey made at a 11 point" behind this critical ramp area will reflect poor conditions (low speed and relatively low volume) without a direct assoc1ation with the cause of the congestion being possible,

Motion picture study procedures provide the advantage of having a view of a reasonably long section of freeway and reasondbly predse measurements of numerous traff1c characteristics such as speed, volume and density However, even with the view of a section of freeway 1000 to 2000 feet in length, it is often difficult to determine accurately the cause of congestion, Congestwn at one study area may actually be caused by conditions existing at a point farther along the freeway, Al­though the motjon picture prov]des some possibilities of contjnually examining cond1tions throughout a section for poss1ble influencing

· factors.· the sectwn studied from a single camera location is not always long enough to reveal whether congestion and "stoppages" are caused by cond1Hons wlthi!"' the study area or by conditiOns ahead,

Two methods which have been successfully utili zed and that do not rely on point survey data for describing flow characteristics are television camera surveillance and aerial photography, Pursuant to this research, two types of aer~.a1 photography have been studied 10: (1) strip photog­raphy where two contmuous pictures are taken simultaneously over the entire study sectlon; and (2) time-lapse ·photography where ind1vidual overlapping pictures are taken at short intervals of time, Time--lapse photography seems tc be more smted for speed and density measurements, and can provide m\.llLple speeds for each vehicle from which acceleration

-31-

can be calculated, Of course, the shortcomings of the aenal approach,. though distinct from the point survey approach 1 are nevertheless signi­ficant in that it is essentially an "instant" surveyo

By careful design of a freeway study, eHher "point" or "instantu surveys can be used to give continuous coverage in both time and space, Thi.s two-dimensional interpretation is indispensable because all traffic characteristics vary in both time and space, "Contour maps" provides a means of illustrating these two-dimensional variations in the characteris­hcs, These maps are drawn by using time as the ordinate, and distance along the freeway as the absclssa a !f aerial photography is used (the "instant I! survey approach) flight runs must be made at per~odic intervals (say 10 minutes) and the speeds are averaged at say 600 feet intervals giving about 3.; points per mile per 10 minutes, Interpolating in both time and space and connecting points of equal speed yi.eld a speed contour map, Obviously, the same contour map could be obtai.ned by i.nterpolating between "point" surveys spaced at 600 feet intervals, F.igure 14 illus·­trates speed contours for total inbound traffjc on the Gulf Freeway 1

Houston 1 obtained from the aerial photographic survey method,

In addi.tion to providing a continuous record of speed for an entire facility for a sustained period such as the peak hour, the contour map affords the opportunity to isolate critical locations and periods and then study them in more detail, Consider .. for example, the Telephone Inter­change Entrance Ramp located at Station 150 + 00 (F.igure 14), The profile of section A-A is plotted in Figure 15, A speed-flow relation, obtained solely from contour maps s is illustrated a A profile plotted from section B-B' in Figure 14 is plotted in Figure 16" This profile illustrates the performance of the entire facility at 7~25 a,m,, as reflected by speeds.

Although profiles at either a poi.nt or at an instance may have some conceptual appeal to the engineer in evaluating freeway operations 1 the level of service concept previously discussed is based on the driving conditions afforded an mdividual motorist as reflected J for example 6 by his speed .. SecUon C-C on Figure 14 indi.cates the path of a hypothetical motorist traver sing the freeway starting from the Reveille Interchange at 7~ OS and arriving at the downtown distribution system at 7:15 a This pro­file i.s also plotted in Flgure 16,

It is generally accepted that the largest number of vehicles that can pass a given point in one lane of a multilane highway 9 under ideal condi­tions u is between 1900 and 2200 vehicles per hour a Thi.s represents an average maximum volume per lane sustained during the period of one hour.

-32-

I.&G.N. RR SCOTT ST.

I 60

CULLEN H.B. 8 T. RR

~\\ ~

i I A n:7T

::- b

DUNBLE H.B. &T. RR TELEPHONE

-+--A

~ i c::::=:= ,- ..J ......r- I __ r;::?~:f­

i .. ~ j .J---+-.___ I __..,1-46-70 so 90 100 110 120 130 140 ISO

WOODRIDGE -i!r;: GRIGGS,

II L

-t==--q--- =ti=--t! ----:fF===~-~ ::=r~~~+~ ·-: ---~

i

~ I 1 I, I .. ....__.~t~~~~ 210 220 230 240 250

SPEED CONTOURS (TOTAL INBOUND TRAFFIC)

FIGURE 14

260 270 280 290 300

% 0.

~ Q w w CL rn w (!) c a: w ~

70~------------------------------------------------~6500

60 ,----, 6000

I \ I \ I \ I

I \ 50 ,--..J \ r-- 5500

I \ / I c / I \ /

I \ / -/ :z: \.... _ _/ 0. 40 I 5000 ~

I RATE OF FLOW ( 3 LANES) ~ I (TAKEN AT SECTION A·A OF FIG. 20) 9 I ~

I ~ 0

I 4500 ~ 30 I

I I I I AVERAGE SPEED (3 LANES)

20 I (TAKEN AT SECTION A·A OF FIG. 14) 4000 I

I I

I 10 3500

o~------~---------~-----------~-------L--------~------~3000

6:45 6•55 7•05 7=15 7:25 7:'35 7:45

TIME OF DAY (A.M.)

SPEED-FLOW RELATIONSHIP AS OBTAINED FROM

CONTOUR MAPS

FIGURE 15

-34-

"' a:

I w ()1

I

t.a G.N. RR SCOTT ST. CULLEN H.B. aT. RR OUMBLE H. B. aT. RR TELEPHONE

~\\ ~

~ - - --.. ~ 31.5

~ :----- ..-:::: ~- ----1----- ~ ~30 - -, ~- --- I -· - ---- 1---...:::::-r-

-""'"" '\) ~------QJ 22!5

I l

~ (5.

IS) T.5.

STATION 20 30 40 50 60 70 80 90 100 110 120 130 140 ISO

\WAYSIDE BRAYS BAYOU GRIGG' L .. ,,.,., ~ ~ .. "# G

l :::: ./

-, - ....... .......__ l L. 1 \ ) P' ~ ~Cjj ~ \ \ I ~, --I,Y

~ Sech Pt?_ c-~ ./?om 'ciq.J4t [5peea o/ mb'ound r; 7otort~ t-r.·o=. TO 1/~ ~A.U)-~--- ....... 30 k .......... .........

~---- ~------ ---- ----- .,.,..-._ ___ -- --..,. / Z2f. ............ ~ I ----- ----------~ ......

\5. l5echon 8-8/4-. pm.liq. '4 (5pc l:::'d5 0 ~T25A lvf)_/ i ........._ -- :7.5

160 170 lBO 190 200 210 220 230 240 250 260 270 280 290 300

SPEED PROFILES OBTAINED FROM "CONTOUR MAP"

FIGURE 16

Figures 17, 18 o 19 J and 20 illustrate volume contours for the three inbound lanes on the Gulf Freeway I Houston, as well as the three-lane total for inbound traffic o It is evident that higher rates of flow exist for specific lanes or for short periods of time 0 Although the capacity of a freeway under ideal conditions is considered to be 2000 vehicles per lane per hour a

only in situations where the peak period demand extends very nearly for the entire hour will this capacity value be realized,

In order to illustrate the speed-density-volume relationship over shorter sections of freeway, the 14 graphs of Figure 21 were plotted for the inbound shoulder lane o Each graph represents the average condHions encountered throughout the study hour for the 2000 feet length of freeway directly above the graph o The graphs o ordinate is speed in mHes per hour and the upper abscissa is volume in vehicles per hour,. while the lower abscissa is density in vehicles per mile. The numbers from 1 to 6 refer to the times of the 6 flight runs 1 thus giving a chronological plot of data, The speed-density relationship is shown by a dotted line; the speed­volume relationship is shown by a solid line,

It is apparent, in studying the graphs in Figure 21, that almost without exceptions increases in density are accompanied by decreases in speed. For the graph covering the interval within the Reveille Interchange, the range in average speeds varies from 45 to 5 mph over the study hour o At the ,other end of the freeway, however, average speeds remain at from 40 mph to 3 5 mph during the same period o The range of average speeds plainly decreases throughout the morning peak hour as one travels toward the CBD on the facility 0

The volume-speed relationship is more difficult to explain. Decreases in speed do not always accompany increases in flow Q However, several of the graphs exhibit a characteristic parabolic loop resulting from the decrease of speed at excessive flows o Keese u Pinnell and McCasland2

explain that as peak flows build up, the average speed drops and generally does not recover to the original relationship with volume until the peak flow or demand has passed. Ryan and Breuning 11 utHize the. concept of critical vs, noncritical flow u with the dividi.ng point being the maximum flow, They report that all three relations among speed, volume and density are linear within the noncritical flow region (before congestion sets in), May, et.a1. 12 define 3 zones which may be described as constant speedu constant volume and constant rate of change of volume with density, In zone 1a the speed of the vehicle is determined by the facility itself and the volume matches the demand. Zone 2 represents impending poor opera­tions; average speed drops but the flow rates may be sustained at a high level. In zone 3 both speed and volume rates decrease 9 which in itself

-36-

I w -....]

I

t.a G.N. RR SCOTT ST. CUU.EN H.B. aT. RR OUMBLE H. B. aT. RR TELEPHONE

~ ·ts5 V / 7 \~~·~ \ I "--~ ~ ""' !/&00 ::! . / C -- ....... " ..... D ! ' •wo... / \ [\ \ ( ' '1"'25 <..... t-.... J-\\.--:f;::::::; J:::t::~:o.::ti:--:;;;;;oo.L-f j,..__/~~t=:::::;;T--t--t----tt--~.;:---~::::::1 ~ : •.-v f\ ~'-. C~J /((c•7.b0-?0!_ _~__.-M>Oo+- ) j ""' ~ ~ 7 . ...., F---..."'\ \ r· 1<1po _ , ::--v ~ =:::::t-" __., (p-- ...).__ '"'-' 1

() 7:0Sf ~ \. I /1-:too:'- ~1'-... (' : 7 _.......r-- I ' / l '. ---1-'\-=---1 ~ . '-•so:r' "'~ "' \ I \.._ ' ~ / ~ ./ )/"" loco-R I"UJO . ) i ·14..V' i ~5?' ~ ~

55 :=:1 L."'\ \{ I r?~ 1\ 1 f//"1 -;;-G-0~4«)\ 'I I i STATION 20 30 40 50 60 70 80 90 100 110 120 130 140 150

, / \~"'" ,..,, i'""" ""7 I """j""" """''#~ , / "- I "- { / -;; \ lp--" ~ ~. c; / ....._

\ \ 1 ~/~~~---1--t-.~ ~w;'J I I ~t--._ \_~ I \ ~~--JP / t!CX>) 11:~

cKoOOJ . ( I \ ! ~ ~bOClOJ I t"'l\\ (~0~:~· !r-f-,4o0•--, rl400j! r'ii;;;~ IY ~·1o00 , )_1::-..... ~oo v __....., ""- ~~<><?o~;:,! r--.. l --r---. '-...._ i -- : '---.._ '-=;' i - ~ .l-"-00- 1400~11 ,......__~ '--~ ~ •

- ; '-... "\ ' "'\, I , ,.- .......-_ . I '""'.._-....... :::;::.;:::::::7:0 ·~-1/""''-~n /'I'~ r--. _/ / f-- r:-=~oo~ \.._.~ ~·-.tf7 / ~ -- -/,oao-R\ / v _,. j-~~ .~>:~~ ' /' ~.!'~(~

_160_ _ ~~-•eo 190 200 210 220 230 240 2so 260 270 2eo ______ 290 300

VOWME CONTOURS (SHOULDER LANE)

FIGURE 17

I w CXl I

I.SG.N.RR SCOTT ST.

BRAYS BAYOU

l

CULLEN H. B. aT. RR

~\\ ~

GRIGGr

1

VOWME CONTOURS (CENTER LANE)

FIGURE 18

OUMBLE H.B. ST. RR TELEPHO~E

I w (.!)

I

160

1.8 G.N. RR SCOTT ST. CULLEN H. B. 8 T. RR

~\\ ~

VOIDME CONTOURS (MEDIAN LANE)

FIGURE 19

OUMBLE H. B. ST. RR TELEPHONE

I ,!:>. 0 I

I.SG.N.RR SCOTT ST. CULLEN H.B. aT. RR DUMB I.E

--+-----\\~~-~"'1

'

I sTATION 20 1 ~ · • 4~· ' ~ 60 10 a~ ~9b-~~~~i~o 110

--- 260

VOilJME CONTOURS (TOTAL INBOUND TRAFFIC)

FIGURE 20

H. B. ST. RR TEl.EPHONE

I.S GN RR SCOTT ST CULLEN H. B. aT. RR OUMBLE H.B. aT. RR TELEPHONE

1800 ~I~~ 1 +=lOW r 500 : 1'500 '-Oo · T I 0 50~ I

,II ~ r CO..Cco-lTK~T.o>J \ I I , ~ ·~·C ·ap~7-t-~~i1~~==~--~~~~~~r-~~~~-;~i-~'=~~~==~ 1 • ...Vr "'I II ~ 1

I ~ t "* .:~;:.-~ 30~'--------------1~-----,------4-------7

I a t Ja"':~!..O;f. l I LU zo· 2·~-~A;-~M;·---+--~--~' -------+-------~------+-------+-------+-------+-------+-------~------~----~~ I I '' ;-------:,--~ . . I cr t 4-· 7:Js A.I.A. . I '"' 10' "' - - I I ...., l ~ I

:£9~CEN. f i ,u_L 11::{.5 I ....... I . ·-··- I ~-r,... .. •. - I ' . I 1 I

I \WAYSIDE BRAYS BAYOU GRIGGSff

,j:>., I • l ,f

~ ~ '. > --=- ~~: ~ I: §§ =27 I ~ ' ~<2 ;: \ s 2 ' ,j c:: v K :;:: C7 J il , n

!I

1'500 54 1'500 1'500 15'00

I f =;j··,~ I : 'r I -,, . ~ ; "-. I t' :3 fo \I - ( ,:~ 5 /I -, . " '~ ' ~ :..u,.:__ " ~ \' 1 ' ) \ '"'-'I ' ' I \ ~ ! : \ ; ~ I '\. I !-~; \

'\ i ,.,'"

1'-1

! vdo.1 ~7,.2 I ......!J1:.5 37.'3 111-5 1.~.5-r,.s I, 11}.5 I 31,.'5 I IIJ.S I !1'1,.'5 .. I ,.J.-. I -:1:·- 1 .. ,.- , -.,..,.. ",. .. T- ·r ... ,

OBSERVED SPEED- VOLUME-DENSITY RELATIONSHIPS (LANE 1) IN TIME AND SPACE

FIGURE 21

may serve as a definition of congestion.

The analysis of highway traffic is more than the making of measure­ments and collection of facts. Although this exploration of the true nature and characteristics of freeway traffic is the necessary beginning in providing new ways of improving performance, the freeway traffic phenomena is so complex that a collection of bare data tell us a little more than we already know. Earlier in this article, a hydrodynamic model was explained, ·An important aspect of this model is the momentum-energy analogy which is summarized in Figure 13. These concepts yield several parameters which provide the means of organizing and interpreting the traffic characteristics collected.

Using Figure 2 2 as a model, volume vs. speed and (volume x speed) vs volume data were plotted, for lane 3 of the Gulf Freeway, inbound traffic during the peak hour. The constants for a curve of the form

was calculated by fitting a regression line to speed-density data taken from aerial photographs. Values of free speed, uf, and jam density 1 kj 1

are 60,3 mph and 133, 1 vpm. Thus, the equation of the curve in the q-u plane becomes

q = 133.1 u- 2.21 ua

The equation for the 11 energy" - speed relationship is

qu = 133. 1 u ~

It can be observed that the curves provide excellent estimates of the points plotted 1 and verify the theoretical approach to the capacity-level of service concept suggested by the momentum-energy analogy of the hydrodynamic model of traffic flow.

(2 2)

(2 3)

(2 4)

The hydrodynamic model, so useful in describing the level of service-. capacity concept 1 can be extended to aid in the explanation of a bottleneck9 . A bottleneck is a stretch of roadway with a flow capacity less than the road ahead (Figure 23). The upper q-k curve in the figure is for the roadway ahead of the bottleneck, and the lower one refers to the bottleneck itself. When the traffic voiume reaches the capacity of the bottleneck, the velocity in the bottleneck, u , is less than ahead of the bottleneck, u . However 1

1 ~ this difference in speed is not significant in urban area capacity problems

-42-

I ~ w I

~I: 0 X :t:

a: LLI a.

(/) LLI ..J

i -:1

0 LLI LLI a. (/)

48

I X

OPTIMUM SPEED(um" 40) BASED ON MAXIMIZING "KINETIC ENERGY" OF TRAFFIC STREAM ~----------------------------------------------------------------------~

I !x X

)(

)(

3f6 r XI

OPTIMUM SPEED (u ... = 30) BASED ON MAXIMIZING "MOMENTUM" OF TRAFFIC~ STREAM ------------------------------------------~----

1

I /1 : I

24

MOMENTUM - SPEED RELATIONSHIP

12 q •133.1u - 2.21uz

I lx I I ~

I I I I

ll.l I !Jol >ol ffisel en • I ::;:ll.ll ::>~I :;:_~I t;:gl o I

I

X

I I I I

ol OJ 21 • I >-I !::I

~· 0.1 51

I ll.ll _II

~I cnJ :r·

72,000 48,000 24,000 800 1200 1600 2000

FLOW-SPEED,qu(VEHICLE MILES/ HOUR2 ) FLOW, q (VEHICLES PER HOUR)

VERIFICATION OF ENERGY- MOMENTUM ANALOGY FIGURE 22

a: :::> 0 :t:

a: LLI a. (/)

LLI

= ~

:1

0 LLI LLI a. (/)

I ,j::. ,j::.

I

0" I ~ 0 ...J LL

q = f(k) FOR HIGHWAY~

SPEED OF VEHICLES IN ON COMING FLOW, U3

'--sPEED OF VEHICLES IN BOTTLENECK, U2

CONCENTRATION- k

TRAFFIC FLOW IN A BOTTLENECK FIGURE 23

(dq/dk)2·

and should not be used as a criterion for determming acceptable operation, Buto any further mcrease in demand (volume) accumulates as a queue in advance of the bottleneck u and the traffic conditions in thj.s region shHt from those expressed by point 3 on the Hgure to those expressed by point 2 (density changes from k

3 to k:':!) o

When a bottleneck is operating at capacity, the speed of traffic is independent of the geometric conditions in the upstream section.. Since congestion may last much longer (Figure 24) than that interval in whi.ch demand exceeds capaci.ty J it is important that precautions be taken to prevent this, A stipulated rate-of-flow for a 5-minute period can ensure that congestion will not occur to whatever degree of confidence desired by a designer" This is illustrated by the desi.gn curves relating level of service to a 5-minute rate of flow (Figure 2 5), Thus 1 a service volume of 1800 has a probability of ,, 50 of guaranteeing 11 stable flow" during the peak 5-minute peri.od, On the other hand 1 there is a 50% chance of "unstable flow" occurring; and a 2, 5% chance of "forced flow" o

Of course, 11 forced flow" is congestion} and "unstable flow" can lead to congestion} due to the statistical vanability of vehicle headways, It is interesting to note that a relatively small reductlon of 100 in the service volume, to a flow of 1700 vph. greatly increases the probability of majn­taining "stable flow" o These curves represent an attempt to put such a dec'j swn in the hands of highway administrators and designers.. After this choice is made J the service volume to be used for design for the peak hour would be obtai ned from Flgure 1, depending on the populat~on of the city, (See Table 2~

Figure 25 was obtained by determining the probab1Jlty of getLng observed rates of flow greater than the predtcted values ut11Jz;ng the data shown m Figures 2 and 3 and assuming the errors are ncrmally dtstrubuted, The first four columns in Table 2 are taken d1rectly from Flgure 25; the last four columns utillze the peaking relationships ex­pressed m Flgure 1,

-45-

II) ~ ..1 u !f ~ > .... 0

a:

I :l z

~ > t= "' ..1

5 :l u

Cl) ~ ::1 3 0 >

200

en 100

i :i I .,

50

0 7•00 AM

2000

1500

1000

BOO

1tl0

7•00 AM 7•10

DEMANDS::.. CAPACITY • 30 MIN. ----------------

7:20 7•30 7•40 7:50 8•00 DURATION OF CONGESTION • 45 MIN,

/ /

" / /

/ /

" , __ .... ,. .... ,167 VEHICLES

" 5 MIN.

" ,. / ,.

"' / ,. ,. , ,.,."(__CAPACITY • 1611& • 2000 VPH

" " ~

7•30

TIME

7:40

RELATION BETWEEN DEMAND, CAPACITY AND CONGESTION

FIGURE 24

-46-

1.00 SEE FIGURE I FOR RELATIONSHIP

/ BETWEEN PEAK 5-MINUTE RATE

(!) OF FLOW AND PEAK HOUR VOLUME. z .90 a::

:;:) 0 X

w (.) .eo > a:: w w :::i!

en i= 11..

lL .7 0

oo fl. 0 0

10

~a: ww >a. .60 ww ...Jt- ZONE OF en=> STABLE FLOW :;:)~ 0~ .50 -, a:: tO ~ ZONE OF ~ UNSTABLE FLOW (!)~ ~a. .40 ~w ~~ m 0 lL 0

>-.... :J m <( m 0 a:: a.

w ~

.30 i= 11.. 0

fl. ,..:

.20 .,.

X w X :::!: i=

.10 ~ :Z:IONiE;: ~

FO!U.ED FLCJW

01500 1600 1700 1800 1900 2000

RATE OF FLOW PER LANE DURING THE PEAK 5-MINUTE PERIOD

DESIGN CURVES RELATING LEVEL OF SERVICE TO FLOWS DURING THE PEAK 5-MIN.

FIGURE 25

-47-

TABLE 2

FREEWAY CAPAClTY WITH CONFIDENCE LIMITS

Approx. ProbabHHies of Var)ous Freeway Design Service Volume (Total Hourly Vol ,/Lane) Peak 5-Min Flow Types of Flow in Peak 5-Min Population of Metropolitan Area

(VPH) Stable Unstable Forced 100,000 500,000 1, 000 000 5,000.000

1500 1.00 0.00 0.00 1100 1200 1300 1300

1600 0.98 0.02 0.00 1200 1300 1300 1400

1700 0. 8 5 0.15 0.00 1300 1400 1400 1500

I 0.02 1400 1500 1500 1600 ,!::>. 1800 0.50 0.48

0)

I

1900 0.15 0.69 0.16 1500 1600 1600 1700

2000 0.03 0.47 0.50 1500 1600 1700 1800

APPLICATIONS

Freeway Design

Highway design is an engineering functi.on--not a handbook problem., The engineer i.s faced with the problem of predicUD:g trafftc demands in future years and providing faciU.ties th.at wHl accommodate that traffic under a selected set of operating conditi.ons or levels of service 0 Too often highway design has been accomplished by adopting a set of hand­book "standards" which when coupled with traffic "guestimates" have resulted in the construction of many seriously inadequate facilities,

Traffic prediction.' trafHc operation and des:gn have now developed ~o the point where H ls possible for engineering (the appUcation of sci.ence) to produce rather reliable results,

A freeway is not built for some date 20 years in the future o It must go to work the fjrst day and serve efficiently all through its expected life. And, if history is not changed, many will be serving for quite a number of years beyond the "design" year.

The freeway is only one facHi.ty in a network of system of streets and highways, It has its place, but the system as a whole must be made to function efficiently. The day has gone when a freeway can be designed wHhin the confines of two parallel r.~ght-of-way lines, Likewise, the day has gone when on]y the 2 0-year "complete system' can be considered when design:ng a parti.cular facility. Traffic projections and designs must be made on partial or incomplete systems :f desirable service is to be obtained in the years before the whole system is completed, With the modern tools avai.lable 1 the designer should have at his disposal an accurate estimate of traffic demand for each stage of completion of the planned system,

Eng~ neer:ng and management must be coupled in the selecUon of a level of servj ce for design that is best adapted to the specific need. Economics and other factors will continue to play a major part in facility programming and even in design; but realistic projected service analysis will lead to more realistlc priority programming.

The largest number of vehicles that can pass a given point in one lane of a multilane highway} under ideal conditions 1 is between 19 00 and 2200 vehlcles per hour. This represents an average maximum volume per lane sustained duri.ng the period of one hour. Studies have found higher

-49-

volur;es for s pecifj c lanes or for short time per~ods" Where at least two lanes are prov:ded for movement in one direction, and d.:.sregarding d~s~ tribuUon by lanes; the capac.ity of a freeway under ideal cond.:.t:ons :s cors~dered tc be 2000 vehicles per lane per hour.,

Where ccnd:tions are less than ideal because of reduced -N:.dtrs: s ~?ht d:.stance. grades and commercial vehl.cles, etc.,·' the c:ipac::ty w~ ll be somewhat lower, Moskowitz and Newman 5 suggest so~e correct:or value tc be used when these condH~ons are anticipated"

When the traff:;.c volume equals the capacity of a freeway, operati.ng condltions are poor" Speeds are low, with frequent stops and high delay" :n order for the highway to provide an acceptable level of service to the road cser! H is necessary that the service volume be lower th:J.r. the c apacHy of the roadway"

The level of serv~.ce approach establ.ishi.ng levels of cperat1on from free flow to capacity wh]ch is being considered by the HRB Capacity Committee is des1gned to allow the engineers and admi.nj strators to pro­vide the highest level of service econom1cally feasible" The morPentum­energy analogy der)ved jn the previous section 1s an effort ~o explain +.he capac~ty-level of. serv~ce relationshtp rationally and quan+.:.tat:veJy.. !Table :3 v) it rr.t.:st be recogr...lzed that h~ghway traffic represents a s:ochast:c ph~?nomenon. Therefore, any h1ghway facUity .. des~gned to accommodate traff~c, must be desi.gr.ed with the realization that from time to t:.rr.e demand wHl exceed capacHy" The organization of Table 2 is useful in that H pro­vi.des the desjgrer with confidence limits in determining t.he nurrber of I!!aln lar:es reeded en a freeway"

After the determinaHon of the number of freeway lanes, the operating condHions at criUcal locations of the freeway must be i.nvesUgated for the effect on capaclty and level of service. Unless some designated level of servl.ce 1s met at every point on the freeway, bottlenecks will occur ar.d traf:hc operation will break down. Critical loc.aUons on a freeway are mani­fest by either sudden ]ncreases ln traffJc demand~ the creati.on of i.nter­veh:cular confl:.cts within the traffic stream, or a combi.naUon of both, An entrance ramp is an example of the first type of critical locaticn, whereas exi.t ramps and grades can cause intervehicular conflicts 0

It is interesting to note that a distinction can be made between the terms '1 cri.t:!.callocation11 and 11 bottleneck 11

0 A·bottleneck is a section of roadway with a capacity lower than the adjacent upstream sectiono Thus,

-50-

I (}1 I-'

I

TABLE 3

LEVELS OF SERVICE AS ESTABLISHED BY ENERGY-MOMENTUM. CONC_EPT

Level of Service Zone

A- Free Flow

B, C & D­Stable Flow

E 1 - Unstable Flow

E2 - Unstable Flow

F.:..Forced Flow

Description

Speeds controlled by driver desires and physical roadway conditions. This is the type of service expected in rural locations.

Flow concentration, speed -l. The conditions at uffiand k' m are acceptable for urban design practice. The divisions between B-C and C-D are arbitrary.

A small increase in demand (flow) is accompanied by a large decrease in speed leading to high densities and internal friction which contribute to instability.

This type of high density operation can not persist and leads inevitably to congestion.

Flows are· below capacity and storage areas consisting of queues of vehicles form. Normal operation is not achieved until the storage queue is dissipated.

Zone Limits Upper Lower

(See Figure 13}

uf . 9uf, . 3 Sqm

.9uf, . 3 Sqm I I u m, q m

I I u m, q m urn' qm

urn' qm I q' . Sum' m

I I . Sum, q m 0

the volume input can exceed the capacity of the bottleneck, and the road­way upstream becomes a storage area whose level of service and rate of flow are governed by the capacity and operating conditions through the bottleneck. If traffic backeq up at a bottleneck is required to stop 1 the capacity of the bottleneck becomes a function of vehicular departure head­ways from a stopped condition. Strictly speaking then 1 not all ''critical locations" are "bottlenecks"; a bottleneck is only one form of critical loca­tion. The most i.mportant consideration is that operation in critical sections never drop below the adopted level of service. Often, this can be effected by not allowing the demand on the facility to exceed the bottleneck capacities.

As traffic operations deteriorate, vehicles tend to form platoons. In general 1 "platooning" is a function of the number 'of slow vehicles and the speed of slow vehicles. When an upgrade is introduced 1 speeds are re­duced anc;l platoon lengths increase. Accident, potential and capacity miti­gating lane change maneuvers are a direct result. The percentage of trucks in the stream, as well as the steepness and length of grade, will determine just how adverse this effect may be.

One possible solution to maintainJng a level of service on the grade equal to a level grade, would be to add a climbing lane whenever the passen­ger car volume and speed varies below the adopted level of service, This 1

of course 1 is not always feasible on a urban freeway facility where lane I

reductions present severe operational problems. The policy of restricting trucks to the outside lane (preciicated on the theory that if all trucks are travelling on the outside lane 1 then vehicles on the remaining lanes can maintain the operation levels ·achieved on level grade) ignores the fact that vehicles in the oufside lane will not accept the same level of service as trucks and will attempt to change lanes. It is impossible for adjacent lanes to operate at drastically different levels of service. This influence·.· of the operation of bne lane on the operation of another is a well established speed characteristic and is sometimes called "speed sympathy". Thus, the most acceptable solution to the problem of operating on freeway upgrades is to see that demand volumes never exceed the adopted level of service.

The traffic demand on a freeway can only change at entrance or exit ramps. Two of the most critical points on a freeway will be upstream from an exit ramp and downstream from a ramp entrance, where traffic demand will necessarily be at a maximum. Operating conditions at exit ramps are generally similar to the operating conditions described at an upgrade, but cari be much more severe where there is a back-up from the exit ramp onto the. main roadway proper. Many exit ramps problems could be avoided by providing for the speed reduction on the ramp rather than on the shoulder lane of the freeway. Even where long parallel deceleration lanes are pro-

-52-

vided, they are not used because of the unnatural maneuver involved, Un­fortunately, the close spacing of interchanges and use of frontage roads favor the use of short slip-type ramps, Where a high exit volume slip ramp is used 1 definite consideration should be given to placing yield signs on the fmntage roads, thus preventing back-up· from the exit ramp onto the free­way •.

Entrance ramps may create two potential conflicts with the maintenance . of the adopted level of service of a roadway. section. First, the additional ramp traffic may cause operational changes in the outside lane at the merge, This condition, of course,. ·will be aggravated by any adverse geometries 1

such as high angle of entry, steep grades, and poor sight distance. Second J

the additional ramp volume may change the operating conditions across the entire roadway downstream from the on-ramp, This is particularly true where there is a downstream bottleneck,

There are three basic procedures employed in determining the capacity of entrance ramps, One method is based on preventing the total freeway volume upstream from the ramp plus the entrance ramp volume from exceeding the capacity of a downstream bottleneck. A second method takes into con­sideration the distri.bution of freeway volumes per lane (discussed in the first section of thi.s paper and also treated extensively by Hess 13 ) and then limits the ramp volume to the mergi.ng capacity (assumed here to be equal to the service volume selected in Table 2) less the upstream volume in the outside lane. The third method states that the ramp capacity 1s limited by the number of gaps in the shoulder lane which are greater than the critical gap for acceptance, 8 It is believed that the second method (Figures 5 to 9) is the most practical in designing a new facility, The first method is predicated on knowing the capacity of bottlenecks-- something that is not known in the case of a new facility, Research concerning the third method is now underway; the advantage of this approach is that it recognizes that ramp capacity and operation must be affected by the geometries of the ramps o

The last "critical location" to be considered is the weaving section o

Weaving sections often simplify the layout of interchanges and result in r1.ght-of-way and construction economy, The capaclty of a weaving section is dependent upon :its length_. number of lanes, running speed and relative volumes of individual movements, When large volume weaving movements occur during peak hours 1 approaching the possible capacity of the section 1

probably results are traffic stream fri.ction, reduced speeds of operatwn, and a lower level of service, This can sometimes be avoided by the use of additional structures to separate ramps, reversing the order of ramps so as to place the critical weaving volumes on frontage roads, and the use of

-53-

collector-distributor roads in conjunction with cloverleaf interchanges.

Weaving sections should be designed 8 checked and adjusted so that their capacity is greater than the service volume used as the basis for design. This is consistent with the level of service concept used in determining the number of main lanes and checking the merging capacities at entrance ramps. The determination of minimum length of weaving sec­tion to meet the controlling level of service is illustrated in Figure 26. These relationships were obtained by considering the outside lane use relation with trip length (Figures 11 and 12). Referring to.Figure 26, the maximum number of vehicles that an exit J R , can not exceed Q-R , plus

1 ~ l

the number of entrance ramp vehic esthat change lanes within the merging section.

Figure 2 7 illustrates four steps to be followed in the design of a freeway system o

Step 1 - Determine the peak hour volumes through the application of the peak hour and directional distribution factors to the assigned daily traffic volumes. In an actual problem the Po M. peak would also be checked.

Step 2 - Determine interchange requirements.. It is important that this be done before freeway main lane requirements be investigated, because the number of ramps depends on the choice of interchange. Thus, a cloverleaf mterchange and a directional interchange may have one or two entrance ramps and one or two exit ramps in each direction; whereas diamond interchanges have one entrance ramp and one exit ramp in each direction. If the interchange i.s to be si.gnal­ized 6 a capacity check is made to see if the planned facilities will handle the traffic with reasonable cycle lengths (See Figures 28 and 29) 14 • Should a facility be apparently underdesigned, additional approach lanes may be added or a higher type facility be substituted in its place.

Step 3 - The number of main lanes depends on what service volume value is chosen as the design capacity. The freeway desi.gn service volumes in Table 2 enable the designer to judge what level of service can be expected for a given service volume based on the probability of obtaining various types of flow conditions during the peak 5-minute period. For the purposes of this example a service volume of 1700 vph is chosen.

-54-

I (./1 (./1

I

N LLC:: o-

N

Zw o...~ ._ IDO.S (.)<( zl-=> I.J..::E

<(~ U)I.J..

<( W 0.6L Rz/0 Cl ~ ------------------

w=> (f) ...I (f)0 . w ;> I EXAMPLE a:: I GIVEN R,= 1000 VPH, Rz=900 VPH, Q.. W ; AND ASSUMING THAT THE FREEWAY

i:S ~ 0.4r LANE SERVICE VOLUME CHOSEN AS

;> THE BASIS OF DESIGN IS 1600 VPH

W 0:: (FROM TABLE2), THE STEPS ARE:

~ ~ I. FIND THE ORDINATE AND ABSICCA

::::> OF THE GRAPH

6 w I R2/Q = 900!1600 =.56

;> z I R,/0•100011600= .62 :5 0.21 2.FIND THE MIN. WEAVING LENGTH (L= 2200')

~ I THAT WILL MEET THE DESIGN LEVEL OF SERVICE.

c::r>- I a::~ i ._w -W XC::

i

01 :.I 0::1

I

Q-R,---

~H OF WEAVING SECTIO~ Q=FREEWAY LANE SERVICE VOLUME (TABLE I.)

Rt• VPH ENTERING Rz= VPH EXITING

L•5000

L=4000

L=3000

L•2000

L•IOOO

L•500

w lJ.. 0 0 0.2 0.4 0.6 0.8 1.0

ENTRANCE RAMP PEAK HOUR VOLUME EXPRESSED AS A PERCENT OF THE FREEWAY LANE SERVICE VOLUME FROM TABLE 2 (R1/Q)

DETERMINATION OF MINIMUM LENGTH OF WEAVING SECTION TO MEET THE DESIGN LEVEL OF SERVICE

FIGURE 26

I U1 0)

I

STEP I - PEAK HOUR VOLUMES (A..M PEAK) ; DIRECTIONAL DISTRIBUTION=.2'1

20~0 200

100 600 , ~

2400 100 400

400

zowoo

STEP 2- INTERCHANGE

a:o-_. Coo coo ""'"''

-.-J400~ n~60CR

--'--

---r-IOO~E I u IOOR I

.... a-~: ooo 000 ......

(V= 140G < 1800 (JK)

50¢00 s!af\o 40~50 10~00 400 200 250 2000

250 600 250 300 200 100 500 800

~ ~ ~ ~

2450 ~ 2400 1600 200 300 150 200 150 0 350 400

800 400 500 4000

40WO ~oi;o 3~0 ro\lJoo

REQUIREMENTS (A.M. PEAK)- SEE FIGURES 28 a 29 FOR PHASING a CAPAaTY

o::o-_,

ggg I

m' =::Jsoo R :::J300 ~

o::o-_. Coo Oo., .., .. _

n IX~-' lrtr..J ooo ooo 0.0.0 I ooo

--., 300 R ~nc.t ~ :QO L

10

m.rl .,_ 1.11'\. ---, 400 R

::j2oo~ /~6~~~GE ! :::Jo R t I : ! ! I :::1~gg~ \ _L_ I I'

~;;;;~========~~~====~=::::;==~~~=========l/ :: i t·~========= 'I !

zsoLE i 200 R iW 250 ~.E I 150 R u

j.Jt-cc I -'>-o: oo 0 000 00"' 000

"""'- ,..,.,._ tV' 2150, C,;SO lOK) IV; 1450 < 1800 (O.K)

7~g~E I u -'>-0:: ooo oo "'"'

tV: \ZOO< 1800 \0 K l

5001. r--350RC :iJW

:/ 00 oo

'"'"' I:V=2.100, Cs96 tC.I'()

STEP 3-MAIN LANE REQUIREMENTS- A.M. PEAK (TABLE 2) a CHECK OF CRITICAL LOCATIONS (FIGS. 5 TO 9,a 26) OUTSIDE LANE

4900 1800)

NU~BER OF INBOUND FREEW~Y L.lNES SMSEO ON :7 0 0

MIN. LENGTH WEAVING SECT."'LN- ~BASED ON 1700 VPH ~

STEP 4- ALTERNATE DESIGN WITH RAMPS REVERSED

4900 4400

NUMBER OF INBOUND FREEWAY I.ANES ~ES

1 1000· 1 ~ Ml~ I..ENGTH WEAVING SECT. [FIG. 26)

FREEWAY DESIGN PROCEDURE FIGURE 27

I (/1 -...,J

I

~T ~~~ __) 1~ ~ ~ ) "'\ ; PHASE B \ T r- ~

1-------;

' I r PHAsE c \ T r __) 1~ / \.'-

~ (; PHASE ~T f _)1~ ~ ~ / \.'-1--- PHASING FOR \\ r ~ r CONVENTIONAL DIAMOND~ r .. :'\--

A-ovERLAP C-OVERLAP

_) 1 \._)~ ~

~ ((- --- \'vr= _) 1 '-~)''- ~ ~ _)l\_)~ ~ (( PHASE 0 \ T (

._)1\._____./j\._

----; '

'\ r PHASE s 'T r ' l r PHASE c ' T r _) 1 \.._)~

~"? I ~~ A- OVERLAP

PHASING FOR OFFSET DIAMOND

~\___)~ ~ ;

2

\Tr C-OVERLAP

_)i~!'- ~~.~~~ Jl(r ~~ 7 ~r- --'l ,_ ~r-

JDJ[ J0J[ J1

0T[ )\~Tr ""'\l~Tr ) ,----..,.Tr

J[Ql[ PH···· JlO [ p~ •• , ~[5( ~···· YOr[ -\\ ,-----..,. ~ '~ ' r--\ ~ A-OVERLAP C-OVERLAP 0-0VERLAP

PHASING FOR 3 LEVEL 8 SPLIT DIAMOND FIGURE 28

1--

, o 3600($(K-D)-I:O] o! ~ C=-3600-0I:V

:~: .---_-__ ,.+------------r---_-__ -___ ,.._ -Tr---.---.--.---.-_----.-----..-__ -.-,-__ IT-·-EQUATION OF CUR~ES

1121--- _ t--- __ _ _ -gr- __ ~ _

:1:0804 =---~~ ~~---- -~~~-1-_ll C t \.J.lll'-_-_T-r-~-;-~:-,-~_f_~i_e~-ir[~_~_;_, :-,-•-VA_R_I ES-,.-__J=

I ~ ~ -l \-- -- - --

96 - j H/i I ~ ' 11 i

(f)

92 f-- - . ty- - ~ ~ -~

: ~-- --,--L---'---,--- - ~\~ ~--0 88f----t------ ------ ----z 0 84 ------ ------- --- - ---- ----u w (f) 801----t----- - -------1------

~- -- -- ~v --If! .I t)

--;--j ~

~~

1---

1--

1--

9 'll I -- --- )--~ 76 c-- ---- ---- -- - ------ - ----- - - §/ i I

\

'\ 111

3 LEVEL DIAMOND IO= 32 0

-

w _J

641---- -- -------- --------1-------- -- CONVENTIONAL- --I-­DIAMOND

----1----f-----

-- ---- --·-·------ ---------·--1-----l

~ 62 1/ --IO•I60.

. -------- 1---------+----~----1

u 56;~--- - --- - -- -· -- ----- ---.----L----L---. 1\" --------- --~ "V h I~ ,_ --+ - + · - --- II~ ·1 \ -

:: -----== I / : 1~ ---<-~~ - :: :: :=-~-----\_.. ___ --+--f---1--~ ~1/, ~

36---- OFFSET

DIAMOND / I:O•I2.0

321----f---'---..-----r----'L/-11------ 1----- ------ ------ ··--·

2Bc--- --- --1/- SPLIT DIAMOND

!:0=320

---1-----·-- I~ -'-----,---1-...J ·-- ----- ---1----------+---+---1

1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700

SUMMATION OF CRITICAL LANE VOLUMES- f.V (VEHICLES I HOUR)

DESIGN CURVES FOR 4 PHASE FACILITIES FIGURE 29

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The operating conditions at critical locations must be checked to ensure that the designated level of service is met at every point on the freeway. The critical sections considered in this paper are merging and weaving sections. Figures 5 to 9 provide the basis for determining if the merg­ing capacities at entrance ramps are exceeded 1 where the merging capacity is defined as the service volume chosen in Table 2. Thus 1 since a total hourly volume of 1700 vph is used as the basis for determining the number of lanes 1

then 1700 vph would represent the merging capacity in this procedure. Figure 26 provides the basis for determining if weaving sections on the freeway 0meet the designated level of service.

Step 4- Alternate -designs should always be considered. In Figure 27, one alternative is illustrated by merely reversing the order of entrance and exit ramps 1 resulting in 3 lanes in each direc­tion instead of 4 lanes.

The level of service should be "in harmony" along the stretch of freeway being considered. Since operational problems at one point are reflected along the freeway for a distance depending on the volume­capacity relationship 1 it is not practical to consider a lower level of service at one or more critical points I rather the level of service selected for design should be met or exceeded at the critical or bottleneck points. This concept is referred to as balanced design and it is a must for freeways.

Freeway Operations

The freeway motorist expects to have his needs anticipated and ful­filled to a much higher degree than on conventional roads. This expecta­tion can sometimes be fulfilled by the application of capacity considerations to rational geometric design. More often than not 1 however, actual traffic and travel patterns differ from the projected values making constant freeway operational attention after construction a must.

Congestion occurs on a freeway section when the demand exceeds the capacity of that section for some period of time. Because congestion can lower the rate of flow 1 a short period in which the capacity is lower than the capacity of adjacent sections is called a bottleneck. Bottlenecks can be caused by changes in the freeway alignment (horizontal or vertical) or reductions in the freeway section (reduction of number of lanes 1 reduction

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.n lane widths, the presence of an entrance ramp, etc.). Accidents, iisabled vehicles and maintenance or law enforcement operations can :ilso cause temporary bottlenecks by reducing the effective capacity x level of service provided.

Freeway design does not always eliminate the need for sound traffic ·egulation. A reasonably homogeneous traffic stream, particularly with ·espect to speed, is essential for efficient freeway operations. Pedes­:rians, bicycles 1 animals and animal-drawn vehicles are excluded from :reeways. Motor scooters I non-highway (farm and construction) vehicles :md processions 1 such as funerals 1 are also generally prohibited from :he freeway. Towed vehicles, wide loads or other vehicle combinations 3uch as trailers drawn by passenger vehicles which impede the normal novement of traffic may be barred during· the peak traffic hours or during lnclement weather.

Minimum speed limits are being increasingly used and have been found of great benefit 1 particularly on high-volume sections. The effect Jf this type of control is to reduce the number of major accident poten-tial lane change maneuvers. The effects of slow-moving vehicles on both ::apacity and accident experience are so pronounced that a greater use of minimum limits appear probable. There is a need to eliminate all vehicles incapable of compatible freeway operation.

Increasing attention has been given to the possibility of and need for using variable speed control on urban freeway sections as a means of easing the accordion effects in a traffic stream as congestion develops. Drastic speed variations might be dampened by automatically adjusted speed message signs in advance of bottlenecks.

A properly designed entrance ramp with provision for adequate accel­eration should allow the entering driver adequate distance to select a gap and enter the outside lane of the freeway at the speed of traffic in the lane. These merging areas operate best when there is a mutual adjustment between vehicles from both approaches. "Yield" signs impose rather ·dras­tic speed restrictions under the laws of a number of states thus causing operational problems, and are no longer mandatory on the Interstate system. It is generally felt that any speed restriction or arbitrary assignment of right-of-_way should be avoided unless inadequacies in the design make it imperative.

It is generally agreed that one key to significant progress in operation of urban freeways lies in improved surveillance techniaue. In its most basic form 1 urban freeway surveillance is limited to moving police patrols.

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Recently, helicopters have been used for freeway surve) Hance in los Angeles and other communlttes o Efficient operation of high density freeways iss however a more than knowing the locahons of stranded vehicles; it may require closing or metering entrance ramps" or ex­cluding certain classes of vehicles during short peak periods 0 There­fore, what is rreeded is a reliable, all weather source of surveillance information with no excessive time lag 0

Experimentation with closed circuit television as a surveHlance tool was initiated on the John Co Lodge Freeway in DetroiL This offers the possibility of seeing a long area of highway in a short or instantaneous period of time,, made possible by spacing cameras along the freeway so that a complete picture can be obtained of the enUre section of roadway o Eval.uahon of the freeway operation depends mostly on the visual interpretation of the observers, However 1 many traffic people believe that this is not enough., The Chicago Surveillance Research Project~ for example, is predjcated on' the assumption that trained obser­vers offered no uniform objectivity., !n other words,. if an expressway is operating well,, this quality can be detected by observing operating characteristics , When the characteristics drop below a predetermined level, action may be taken.,

A traffic surveillance system should involve the continuous sampling of basic traffic charactenstics for interpretation by established control parameters 1 in order to provide a quantitative knowledge of operating conditions necessary for immedjate rational control and future design, The control logic of a surveillance system, or any system_, for that matter is that combinatlon of techniques and devices employed to regulate the operation of that system, The analysis shows what information is needed and where it will be obtained, Then_, and only then, can the conception and design of the processing and analyzing equipment necessary to convert data into operational decisions and design warrants be descr~bed.,

Jn research conducted durmg the past year by the Texas Transportatl.on Institute on the Gulf Freeway Surveillance Project 2 the application of many control parameters to the descriptwn and eventual control of freeway con­gestlon was explored, Figures 30 and 31- illustrate the operation of the 3 inbound lanes of some six miles cf the fac~lity during the morning peak hour as obtained from time-lapse aerial photographic studies, Four control parameters_, derlved in the previous sectwn _, are superimposed on the con­tour maps: (lJ the speed at possible capacity, urn; (2J the density at pos­sible capacity_- km; (3) the speed at the opUmum servlce volume u m; and ( 4) the dens1ty at the optimum service volume k' m, These parameters afford a rational,, quantitative means for describing the level of operation

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I ())

N I

1.8G.N. RR . H. B. aT. RR DIJNBLE H.B. 8T. RR TELEPHONE

~\\ ~

'S T'M~40-- "--- -r-~~ld~_otl~IPr'ble (:fpacilj~ ' /"' ~ · ~ (!/ !) ~ I )( v-~~-·~ •~v~ ~ ) ~./

:;::,., r.:z.os ~ tUr 5.fg.f!/e l..f::low-::;>--.160-r- I /-- r ---1'--.. '-. ~ \40.._............-r--~ 1-40 I ,... ""!) \ V ...... _,. ..... _........._ I ~ ..-----"-~ T:l5 v I . 1'--140........ ..... I - --1-- 'IOV-

~ T:os · ...... J1:::.~==-:-----t'--nens,h,l af {j)_ipftmum ~rvtce 16/.~r _ 140 I <1.1 --=~- ---J v'oa- - 1 I .......... -~ ~5'5' ~5. able 4. - J. / ' ... =l::.s4-o-~ ( · f 1 &.,ro p/e +lo ~ !t 100-+-----..1

STATION 2.0 30 40 . 50 60 70 80 I 90 100 110 12.0 130 140 150

. \WAYSIDE BRAYS BAYOU GRIGGs;; L r wooqRIDGE REV£~'(\ ~ _ ""' l , r " -:/11 -~ :_~~' \ '\/ f" ).« ~ 1~7<~

! ~~/ -............... I " ..... _ 1\~--'~£/.Gi.!../ ~f\ I ~UJ) \

'-.....k"0e11~vly{o-fAw,Ne ~pdc. tY) / --J:r-_l ~ ~ ~ \ ~ ~: ,_ - ' ..... ._ "--:lAo-~- f --'Wt:!!!,foile/.Cto"fl..,_::- --:;~ ~.::..._ .... ,"'::_~ "'"'~~ .... _ :

1

~ ---· - - ·;.. ' .).-.:::;:::;:-1 ~, ,.:> ...,. iJ'!l -- - -•eo.:.....- ! ~-- -- 1---:::..:::::::r- ,-r--(... '---240 ........... --;:.:::; ---:=.,.o

r---140- -- - -- --.I 1- - -· ·-.:::::---1 -....... - - -iS0:::::..-::~40="'- - .)~ ----:::, ........ ~ .1"1- J .J .r. c::;-, ...., I /. l I ~- / -:::::~__.:.:::.- - ·= _..- ~J?;!!r;t <U '-rf-'' "•~• _..__!::;_, Y • (. VV/• fC - _.. /

----- ~ 1 100 I _.!.-::_ fa/:?(e .-f ~w.~r:--. -.:--'-0 --160 · 170 180 190 2.00 2.10 Z2.0 2.30 I 240 250 260 270 2.80 2.90 300

DENSI1Y CONTOURS I (3 LANE TOTAL)

FIGU$ 30

I (j)

w I

1.8G.N. RR SCOTT ST. CULLEN H. B. liT. RR OUMBLE H. B. 8T. RR

-.. ~ ~:~~~~+-+----r-=~-+---1-1~~--~----+-----~~~~~~~~~~~~~~~~--~

~ >. 7:215 f.-:o""""...,....>J!!===---\'"7".c._+-'S--=4::;::--:;;o::-..J.--4---S~==---">-l----.:: ~ ~-----4~

~ q,

~ 4:~~----~----~-----+~---q~~--+-----~----~~~~~

STATION .:v 30 40 50 -- --60 70 eo 90 100 110

_lAYSIDE BRAYS BAYOU

~ GRIGGr L

......, .:::: ~ ......... '>,(/ 1 \ ).__P-

\ \

SPEED CONTOURS {TOTAL INBOUND TRAFFIC)

FIGURE 31

120 130 140

TELEPHONE

150

on the facility: stable flow, unsta?le flow and forced flow 0

Figure 32 illustrates continuous profiles of the possible capacity~ qm ,, and the optimum service volume, q' m, which were derived by ap­plying the momentum-energy analogy to speed-density data taken from aerials of the facility. Thus, H stable flow is to be mal.ntained on the facHity, demand must be kept below the optimum service volume. Use of possible capacity as a basis for ramp metering or control places opera­tion of the facility in the unstable zone of operation~ and provides absolutely no safety factor against breakdowns due to statistical variability in demand.

Efforts to measure freeway operaUonal efficiency in terms of traffic "throughput" (momentum} are obviously inconsistent with the level of service (energy) concept~ since maximum throughput must necessari.ly be achieved with a high traffic stream density 6 a low traffic stream speed, and a level of operation typified by "unstable flow". On the other hand~ the optimum service volume provides for speeds 33% higher, densities 33% lower 8 a level of operaUon typified by "stable flow", and with only a 10% reduction in flow. Actually o because there is less probability of attaining "forced flow•s (congested flow inevitably accompanied by complete break­down) 8 the "throughput'' from day to day might very well be higher because of less frequent breakdowns o

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I en Ul I

I.SG.N. RR SCOTT ST. CULLEN H. B. 8 T. RR OUMBLE H. B. ST. RR TELEPHONE

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-.,.

'R .c. ---~--

~ ~~-- '-...La,Pe5 7.2~ - -+--"--~- -+--

~ ~ I)

~~-----,r-----_,------~-------+-------+-------r-------+-------+-------r-------r-------r-------r------~----~

%-\j :6==;-·r- =t ==t- 1 cite ~P ==4 b--- l 4= g; b~b ~ STATION 20

:::-~/

I--I-

30 40 50 60

\AYSIOE BRAYS BAYOU

}

~ \

70 80 90

GRIGG{ L

1' ~ 100 110 120 130 140 150

""'i"' """;!/ ~ :s....:~~ s CZ! ~~~rs~

-l-----t-t---1----t--- =::::t:=----1 JPos~tbk 2f"apac16( - I I I - 17

fl ~ r ~-- -l- - fop}~mJ(1?- se~v~ce voVome-(

FF ==F f f;-4 -t--+---,---f--fSi_J+-~-t-~i---4~~ 160. 170 180 190 200 210 220 230 240 250 260 270 280 290 300

CAPACITY PROFILES (UNEAR MODEIJ

FIGURE 32

SUMMARY

Traffic operatl.on and geometric design are essentially systematic attempts to resolve a demand-capacity relationship for a given faC:JJity i.n a manner that will provide an acceptable level of service to the motorist. This report deals with urban freeway volume (demand) and capacity char­acter] sties, and their application to freeway design and operation.

An important volume characteristic which is discus sed is the distri­bution of demand during the peak hour. Peak rates of flow within the peak hour exceed the average hourly rate of flow on urban freeways, It is important that the peak hourly volume presently used as a criteria for design be expanded to accommodate the higher rates of flow which exist over shorter intervals within the peak hour 0 This is true because a con­dition in which the demand exceeds the capacity can extend congestion for a much longer Ume than just the duration of the peak flow period (see Figure 24). In Figure 1 8 this variation has been related to the size of the city thus affording a means of estimating the highest 5 minute rate of flow during the peak hour on a facility.

Another vital volume characteri.stic considered is the lane use dis­tribuhon of vehi.cles on freeways. The outside lane of a freeway will, on the average, have a lower volume than the other lanes o The most impor- . tant factors influencing the percent of the total freeway traffic in the out­Sjde lane immediately upstream from an entrance ramp are the total freeway volume and entrance ramp volume (See Figures 5 and 9) 0 Other factors are the sequencing of entrance and exit ramps 6 their spacing 6 and their volumes. (See the nomographs illustrated in Figures 6 8 7 and 8).

A second aspect of lane use distribution discussed is the relaUonship between trip length and outsi.de lane utilization obtained through the use of a "Lights-On11 study technique (Figures 10, 11 and 12) o This relationship was useful jn establishi.ng the minimum length of freeway weavi.ng sections based on entrance and exit ramp volumes (See Figure 26).

The second section of this report deals with freeway capacity char­acterjstics o A theoretical approach to pr:oviding a rati.onal relationship between capacity and level of service is formulated utilizing a hydro­dynami.c model and based on an energy-momentum analogy (Figure 13). The theory is verified (Figure 22) and its utility toward a quantitative description of level of service is suggested in the preparation of a table· of Freeway Design Service Volumes (Table 2) to be used in determining

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freeway main lane requirements, Fundamental volume-speed-·densH.y relationships (figure 21) and the]r measurements (figure 14, 15 and 16) on urban freeways are discussed o The importance of the contour format as a means of presenti.ng a complete pi.cture of performance over long sections of freeway and extended intervals of Ume j s also described in this section"

It js signHjcant that the first secUon of the body of the report deals with freeway demand and the second section with capacHy ,, In the third section_, appHcati.ons are made of these demand and capacity characterjstics to freeway operations (Figures 30: 31 and 32)and to freeway design (Flgures 26 :· 27, 28, and 29) featuring a step-·by-step design procedure,.

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APPENDIX

-69-

I -...:i 0

'

APPENDIX A

TABULATION OF THE NUMBER AND MAGNITUDE OF THE TIMES THE DIFFERENCE BETWEEN THE OBSERVED PERCENTAGE LESS THE PREDICTED PERCENTAGE EXCEEDED THE NATURAL DATA VARIABILITY

NUMBER 5 Min. NUMBER OF TIMES THE NATURAL DATA VARIABILITY lS EXCEEDED BY:

NUMBER STATE FREEWAY PERIODS 0-l% l-2% 2-3% 3-4% 4-5% 5-6% 6-7% 7-8% 8-10% 10%

05 Texas Gulf 24 2 0 0 0 0 0 0 0 0 0

07 Texas Dallas 32 2 2 2 1 0 0 0 0 0 ·0

12 Texas Gulf 32 2 0 0 0 0 0 0 0 0 0

13 Texas Gulf; 32 0 1 0 0 1 0 0 0 0 0

31 Texas Gulf 30 2 0 0 0 0 0 0 0 0 0

33 Texas Gulf 30 4 1 2 0 0 0 0 0 0 0

41 Texas Gulf.· 36 ·o 2 0 0 0 0 0 0 0 0

44 Texas Gulf 36 2 0 0 1 0. 0 0 0 0 0

0501 Calif. San Bernardino 35 2 3 2 l 1 1 2 1 0 0

0503* Calif. Harbor 24 4 2 1 1 3 2 0 0 D 0

0505* Calif. Hollywood 30 1 3 5 5 3 3 1 2 1 1

*·· Unusual Geometries (lane dropped or added)

APPENDIX A (Continued)

NUMBER 5 Ml.n NUMBER OF TIMES THE NATURAL DATA VARIABILITY IS EXCEEDED BY:

NUMBER STATE FREEWAY PERJOD_9 0-lJ? 1-2% 2-3% 3-4% 4-5% 5-6% 6-7% 7-8% 8-10% 10% ------ --- ---- -·---- -.-.----

0609 (1) Coloo Valley Highway 24 1 1 0 0 0 0 0 0 0 0

0610* Colo. Valley Hjghway 24 0 0 2 4 3 2 2 3 1 3

1101 Ga. Atlanta Expressway 24 1 0 1 0 1 1 0 0 0 0

1102 Gao Atlanta Expressway 24 1 0 0 0 1 -0 0 0 0 0

I 1103 Ga. Atlanta Expressway 18 1 1 0 0 0 0 0 0 0 0 ""-.]

1--'

I 1104 Ga. Atlanta Expressway 24 0 4 0 0 1 0 0 0 0 0

1105 Ga. Atlanta Expressway 24 1 2 1 1 0 2 0 0 1 0

1106 Ga. Atlanta Expressway 18 2 3 2 0 0 1 0 0 1 0

1107 Ga. Atlanta Expressway 24 0 3 2 2 1 0 0 0 0 0

1108 Ga, Atlanta Expressway 26 5 1 1 0 0 1 1 2 0 0

1109 Ga. Atlanta Expressway 18 5 2 1 2 l 0 0 0 0 0

1430* 111, Congress Street 24 1 5 4 4 2 3 0 0 1 0

* Unusual Geornetrjcs (lane dropped or added)

APPEND'IX A (Continued)

NUMBER 5 Mino NUMBER OF TIMES THE NATURAL DATA VARIABILITY IS EXCEEDED BY:

NUMBER STATE FREEWAY PERIODS 0-1% 1-2% 2-3% 3-4% 4-5% 5-6% 6-7%. 7-8% 8-10% 10%

1503** Ind. Tri-State 30 0 0 0 0 0 0 0 0 0 0

2313 Mich~ Edsel Ford 28 6 3 1 0 1 0 0 0 0 0

2314(1) Mich. Edsel Ford 24 6 3 1 0 1 0 0 0 0 0

2316(1) Mich. Edsel Ford 09 2 3 1 0 0 0 0 0 .0 0 I

-..3 2317(1) Mich. Edsel Ford 35 2 3 2 4 1 2 0 0 0 0 N .t

2318(1) Mich. Edsel Ford 19 2 3 0 0 1 0 1 0 0 0

2321 Mich. Edsel Ford 14 1 0 l l 0 0 0 0 0 0

2322 Mich. Edsel Ford 15 0 2 3 1 0 0 0 0 0 0

2323(1) Mich. Edsel Ford 26 1 0 0 0 0 0 0 0 0 0

2503(1) Mo. Intercity 24 0 2 0 0 0 0 0 0 0 0

3101 N.J. Garden State 30 2 6 1 1 1 0 0 0 0 0

* Unusual Geometries (lane dropped or added) ** Freeway Volume is less than 2000 vph (1) Study with complete adjacent ramp data

APPENDIX A (Continued)

APPENDIX A (Continued)

NUMBER 5 Mino NUMBER OF TIMES THE NATURAL DATA VARIABILITY IS EXCEEDED BY:

NUMBER STATE _F_FEE_y/ Ay __ PERIODS 0-1% 1-2% 2-3% 3-4% 4-5% 5-6% 6-7% 7-8% 8-10% 10% --- ---

3315 N.Y. No Y, State 24 0 0 0 0 0 0 0 0 0 1

222 Texas Eastex 26 2 1 0 0 0 0 0 0 0 0

131 Texas Eastex 18 3 2 2 1 0 0 0 0 0 0

221 Texas Eastex 26 0 4 1 1 0 0 0 0 0 0

i30 Texas Eastex 24 1 1 2 0 0 0 0 1 0 0

I ""-3

3010 Texas Gulf Freeway 16 0 2 1 0 0 0 0 0 0 0 w .I

4020 Texas Gulf Freeway 15 2 0 2 0 0 0 0 0 0 0

5030 Texas Gulf Freeway 13 2 2 4 0 0 0 0 0 0 0

5930 Texas Gulf Freeway 10 0 2 1 1 0 0 0 0 - 0 0

6050 Texas Gulf Freeway 16 0 1 1 1 0 0 0 0 0 0

7060 Texas Central Expressway 13. 2 1 1 0 0 0 0 0 0 0

4413* Texas Central Expressway 36 2 4 4 0 2 0 0 0 0 0

* Unusual Geometries (Lane Dropped or Added)

., ""-.]

~ I

APPENDIX A (Continued)

NUMBER 5 Min~ NUMBER OF TIMES THE NATURAL DATA VARIABILITY IS EXCEEDED BY:

NUMBER STATE FREEWAY __ PERIODS .Q-1% 1-2% 2-3% 3-4% 4-5% 5-6% 6-7% 7-8%

4414* Texas Central Expr. 36 3 1 3 4 1 1 1 2

R12{1) Texas Gulf Freeway 36 3 2 2 1 0 1 0 0

R13(1) Texas Gulf Freeway 36 2 2 1 0 0 0 0 0

GRAND SUM 1212 83 86 61 38 26 20 8 11

Percent of the time that the difference exceeds the Natural Data Variability by a percent more than:

*Unusual Geometries (Lane Dropped or Added) (1) Studies with complete adjacent ramp data

0% 1% 2% 3%

29.1% 22.2%15.1%10.1%

4% 5% 6% 7%

6.9% 4.8% 3.1% 2. 5%

8-10% 10%

8 1

0 0

0 0

13 6

8% 10%

1.6% 0. 5%

REFERENCES

1. U o S. Bureau of Pubhc Roads 1 "Practical ApphcaUons of Research" 1

Highway Capacity Manual 1 U o So Government Printir.g OfLce ~ Washington, D .. C., 1950,

2. Keese, Charles].; Pinnell) Charles; and McCasland, Wo R,~ '1A Study of Freeway Traffic Operations '1 , H3ghway Research Board Bulleu~. 235, Washl.ngtcn .. D. C,J 1960.,

3 o Keese.· Charles J .·., "Improving Freeway Operat~ons'~ J Proceedings of. the Western Section.· Institute of Traffic Engineers. 1960.

4 o Texas Highway Department] Des1gn Manual for Cor.trolled Access Highw..£.Y.§_, Austin_. Texas 1 January 1960 1 (Rev1sed December 1962).

5, Moskowitz, Karl and Newman J Leonard, "Notes on Freeway Capacity" 1

Highway Research Board Record 27 J Washington, D, C,: 1963,

6, Port Development Department} Planning Div3sion 1 11 Route 3 'Lights·-

On: Traff1c Survey", Port of New '{ork Authority, New York 1 1960.

7, Greensberg 1 H,, 11 An Analysis of Traffic Flow" 1 Operat:ons Research 7' (1959) 0

8 .. Drew 1 Donald R., "A Study of Freeway Traffic CongesUon" 1 D1 ssertatlon Texas A&M Univers1ty, 1964.

9, Lighthill 1 M, J, and Whitham. G, B,, "On Kinematic Waves: "A Theory of Traffjc on Long.· Crowded Roads.·· Proc, R..2Y_: Soc. of Londor>_. VoL 229, 1955.

10, McCasland; W, R,. ''Companson of Two Techniques of Aer:al Photographs for Application in Freeway Traffic Operations Studies", presented at 43rd Annual Meeting of the H1ghway Research Board 1 1964. Washington .. D, C,

11, Ryan 1 D" P, and Breuning .· S, M. , "Some Fundamental Relationships of Trafflc Flow on a Freeway~~: Hi.ghway Research Board_. Bulletin 324,

12o May, A. D,; Athol) P,; Parker) W,; and Rudden, J, B,, "Development and Evaluation of Congress Street Expressway P1lot Detection System".· Highway Research Board, Record No, 21,

13, Hess, Joseph W 0, "Capacities and Characteristics of Ramp-Freeway­ConnecUons"" Highway Research Board_. Record No, 27,

14, Drew, Donald R ., 9 tiDe sign and Signalization of H1gh-Type Facillties" .· Traffic Engineering, Vol, 33, No o 10 J July. 1963,

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