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CE 254Transportation EngineeringWes Marshall, P.E. University of Connecticut February 2008The Four-Step Model:
II. Trip Distribution
The Basic Transportation ModelStudy Area Zones Attributes of ZonesSocioeconomic DataLand Use DataCost of Travel btw. ZonesThe Road Network Traffic Volume by Road Link Mode Splits EmissionsInputsOutputs
Whats in the Black Box?The Four-Step Model
The Four-Step Modeling Process Trip Generation
Trip Distribution
Mode Choice
Trip AssignmentWHY?
The Four-Step ModelThe main reason we use the four-step model is:To predict roadway traffic volumes & traffic problems such as congestion and pollution emissions In turn, we typically use the models to compare several transportation alternatives
The Four-Step ModelOriginally developed in the 1950s with the interstate highway movement Since the 1950s, researchers have developed a multitude of advanced modeling techniques
Nevertheless, most agencies still use the good ol four-step model
Overview of the Four-Step Model
Model residential trip productions and non-residential trip attractions w/ - Regression Models- Trip-Rate Analysis- Cross-Classification Models - i.e. traffic flows on network, ridership on transit lines - A matrix of trips between each TAZ also called a trip table - i.e. columns of trip productions and trip attractions
- No. of Housing Units - Office, Industrial SF - HH Size- Income- No. of CarsIterative Process
Land Use DataInput:Household Socioeconomic Data}Examples of HH socioeconomic data}Examples of land use dataOutput:Trip Ends by purpose Input:Trip Ends by purpose Output:Trip Interchanges Input:Trip Interchanges Output:Trip Table by ModeInput:Trip Table by Mode Output:Daily Link Traffic Volumes TRIP GENERATIONTRIP DISTRIBUTIONMODE CHOICETRIP ASSIGNMENTProcess:Survey DataGrowth Factor ModelsNot as accurate as Gravity ModelUsed for external trips or short-term planningGravity ModelUsed for regional or long-term planning Process:
- i.e. traffic flows on network, ridership on transit linesIterative ProcessInput:Trip Interchanges Output:Trip Table by ModeInput:Trip Table by Mode Output:Daily Link Traffic Volumes MODE CHOICETRIP ASSIGNMENTFinds trip interchanges between i & j for each mode- Function of Trip Maker, Journey, and Transport FacilityTrip End ModelMode plays role in trip endsTypically used for small cities with little traffic and little transitNo accounting for the role that policy decisions play in mode choiceTrip Interchance ModelUse when LOS is important, transit is a true choice, highways are congested, and parking is limited Process:Allocate trips to links between nodes i & j- Function of Path to Destination and Minimum Cost (time & money)Identify Attractive Routes via Tree BuildingShortest Path Algorithm or Dijkstras AlgorithmAssign Portions of Matrix to Routes / TreeUser Equilibrium, Heuristic Methods, Stochastic Effects w/ LogitSearch for ConvergenceProcess:
Some General Problems with the Conventional MethodologyHuge focus on vehicular traffic A transit component is typical in better modelsTypically forecasts huge increases in trafficLeads to engineers building bigger roads to accommodate forecast traffic Which leads to induced traffic and congestion right back where we started when we needed the bigger roads in the first place
Some General Problems with the Conventional MethodologyPedestrians and bicyclists are rarely includedLevel of geography is difficult for non-motorized modesNetwork scale is insignificantInput variables are too limited
Preparing for a Four-Step ModelBefore jumping into trip generation, we first have to set up our project
Define study area and boundariesEstablish the transportation networkCreate the zones
Defining the Study Area3 Basic TypesRegionalStatewide or a large metro areaUsed to predict larger patterns of traffic distribution, growth, and emissionsCorridorMajor facility such as a freeway, arterial, or transit lineUsed to evaluate trafficSite or ProjectProposed development or small scale change (i.e. intersection improvement)Used to evaluate traffic impact
Establish the NetworkRoads are represented by a series of links & nodes
Links are defined by speed and capacityTurns are allowed at nodesLinkNode
Establish the NetworkTypically only main roads and intersections are included Even collector roads are often excludedThis practice is becoming less common as the processing power of computers has increased
Creating ZonesCreate Traffic Analysis Zones (TAZ)Uniform land useBounded by major roadsTypically small in size (about the size of a few neighborhood blocks) The State of Connecticut model has ~2,000 zones that cover 5,500 square miles and over 3.4 million people
Creating ZonesAll modeled trips begin in a zone and are destined for a zoneZones are usually large enough that most pedestrian and bicycle trips start and end in the same zone (and thus not modeled)Also, the typical data we collect about zones in terms of population and employment information is not enough to predict levels of walking and biking
Trip Generation
Trip GenerationUsing socioeconomic data, we try to estimate how many trips are produced by each TAZFor example, we might use linear regression to estimate that a 2-person, 2-car household with a total income of $90,000 makes 2 home-based work trips per day Using land use data, we estimate how many trips are attracted to each TAZFor example, an 3,000 SF office might bring in 12 work trips per day
Trip GenerationThe process considers the total number of tripsThus, walking and biking trips have not been officially excluded (although most models ignore them completely)The trips are generated by trip purpose such as work or shoppingRecreational or discretionary trips are difficult to include
Trip GenerationSocioeconomic DataLand Use DataInput:Output:Trip Ends by purpose (i.e. work) in columns of productions & attractions
Sheet1
TAZProductionsTAZAttractions
11219
219212
33534
44438
55545
61066
71374
82282
120120
Sheet2
Sheet3
Sheet1
TAZProductionsTAZAttractions
11219
219212
33534
44438
55545
61066
71374
82282
120120
Sheet2
Sheet3
Sheet1
TAZProductionsTAZAttractions
11219
219212
33534
44438
55545
61066
71374
82282
120120
Sheet2
Sheet3
Sheet1
TAZProductionsTAZAttractions
11219
219212
33534
44438
55545
61066
71374
82282
120120
Sheet2
Sheet3
Sheet1
TAZProductionsTAZAttractions
11219
219212
33534
44438
55545
61066
71374
82282
120120
Sheet2
Sheet3
Sheet1
TAZProductionsTAZAttractions
11219
219212
33534
44438
55545
61066
71374
82282
120120
Sheet2
Sheet3
Trip Generation Trip DistributionThe question is how do we allocate all the productions among all the attractions?Zone 1Trip Matrix or Trip Table
Sheet1
TAZProductionsTAZAttractions
11219
219212
33534
44438
55545
61066
71374
82282
120120
Sheet2
Sheet3
Sheet1
TAZProductionsTAZAttractions
11219
219212
33534
44438
55545
61066
71374
82282
120120
Sheet2
Sheet3
Sheet1
TAZProductionsTAZAttractionsTAZ12345678
112191
2192122
335343
444384
555455
610666
713747
822828
120120
TAZ12345678
1
2
3
4
5
6
7
8
Sheet2
Sheet3
Trip Distribution
Trip DistributionWe link production or origin zones to attraction destination zonesA trip matrix is produced
The cells within the trip matrix are the trip interchanges between zones
Trip InterchangesDecrease with distance between zonesIn addition to the distance between zones, total trip cost can include things such as tolls and parking costsIncrease with zone attractivenessTypically includes square footage of retail or office space but can get much more complicated
Trip DistributionSimilar to Trip Generation, all the modes are still lumped together by purpose (i.e. work, shopping)This creates a problem for non-vehicular trips because distance affects these trips very differentlyAdditionally, many walking and biking trips are intra-zonal & difficult to model
Criteria for allocating all the productions among all the attractionsCost of tripTravel TimeActual CostsAttractivenessQuantity of OpportunityDesirability of OpportunityBasic Criteria for TD
How to Distribute the Trips?Growth Factor ModelsGravity Model
Growth Factor ModelsGrowth Factor Models assume that we already have a basic trip matrix
Usually obtained from a previous study or recent survey data
Sheet1
TAZProductionsTAZAttractionsTAZ12345678
112191550100200
2192122505100300
335343501005100
44438410020025020
555455
610666
713747
822828
120120
TAZ12345678
1
2
3
4
5
6
7
8
Sheet2
Sheet3
Growth Factor ModelsThe goal is then to estimate the matrix at some point in the future For example, what would the trip matrix look like in 10 years time?Trip Matrix, t (2008)Trip Matrix, T (2018)
Sheet1
TAZProductionsTAZAttractionsTAZ12345678
112191550100200
2192122505100300
335343501005100
44438410020025020
555455
610666
713747
822828
120120
TAZ12345678
1
2
3
4
5
6
7
8
Sheet2
Sheet3
Sheet1
TAZProductionsTAZAttractionsTAZ12345678
112191550100200
2192122505100300
335343501005100
44438410020025020
555455
610666
713747
822828
120120
TAZ12345678
1660120240
2606120360
3601206120
412024030024
5
6
7
8
TAZ12345678
1????
2????
3????
4????
5
6
7
8
Sheet2
TAZ123478
1550100200355400
2505100300455460
3501005100255400
410020025020570702
20535545562016351962
6
7
8
TAZ12345678
1660120240
2606120360
3601206120
412024030024
5
6
7
8
TAZ123478
15.656.3112.7225.4400400
250.55.1101.1303.3460460
378.4156.97.8156.9400400
4123.2246.3307.924.6702702
257.7464.6529.5710.219621962
6
7
8
Sheet3
TAZ123478
1550100200355400
2505100300455460
3501005100255400
410020025020570702
20535545562016351962
1804063807401706
7
8
TAZ12345678
1660120240
2606120360
3601206120
412024030024
5
6
7
8
TAZ123478
15.656.3112.7225.4400400
250.55.1101.1303.3460460
378.4156.97.8156.9400400
4123.2246.3307.924.6702702
257.7464.6529.5710.219621962
6
7
8
Avg Factor
TAZ123478
1060100200360400
2505100300455460
3501005100255400
410020025020570702
20036545562016401962
1804063807401706
7
8
TAZ12345678
1060120240
2606120360
3601206120
412024030024
5
6
7
8
TAZ123478
15.656.3112.7225.4400400
250.55.1101.1303.3460460
378.4156.97.8156.9400400
4123.2246.3307.924.6702702
257.7464.6529.5710.219621962
6
7
8
Some of the More Popular Growth Factor ModelsUniform Growth FactorSingly-Constrained Growth FactorAverage FactorDetroit FactorFratar Method
Uniform Growth Factor Model
Uniform Growth FactorTij = tij for each pair i and jTij = Future Trip Matrix tij = Base-year Trip Matrix = General Growth Rate i= I = Production Zone j= J = Attraction Zone
Uniform Growth FactorTrip Matrix, t (2008)Trip Matrix, T (2018)If we assume = 1.2, then Tij = tij= (1.2)(5)= 6Tij = tij for each pair i and j Tij = Future Trip Matrix tij = Base-year Trip Matrix = General Growth Rate
Sheet1
TAZProductionsTAZAttractionsTAZ12345678
112191550100200
2192122505100300
335343501005100
44438410020025020
555455
610666
713747
822828
120120
TAZ12345678
1
2
3
4
5
6
7
8
Sheet2
Sheet3
Sheet1
TAZProductionsTAZAttractionsTAZ12345678
112191550100200
2192122505100300
335343501005100
44438410020025020
555455
610666
713747
822828
120120
TAZ12345678
1660120240
2606120360
3601206120
412024030024
5
6
7
8
Sheet2
Sheet3
Uniform Growth FactorThe Uniform Growth Factor is typically used for 1 or 2 year horizonsHowever, assuming that trips grow at a standard uniform rate is a fundamentally flawed concept
Singly-Constrained Growth Factor Model
Singly-Constrained Growth Factor MethodSimilar to the Uniform Growth Factor Method but constrained in one directionFor example, lets start with our base matrix, tattractions, jproductions, izones
Sheet1
TAZProductionsTAZAttractionsTAZ12345678
112191550100200
2192122505100300
335343501005100
44438410020025020
555455
610666
713747
822828
120120
TAZ12345678
1
2
3
4
5
6
7
8
Sheet2
Sheet3
Singly-Constrained Growth Factor MethodInstead of one uniform growth factor, assume that we have estimated how many more or less trips will start from our origins
Now all we have to do is multiply each row by the ratio of (Target Pi) / (j)
Sheet1
TAZProductionsTAZAttractionsTAZ12345678
112191550100200
2192122505100300
335343501005100
44438410020025020
555455
610666
713747
822828
120120
TAZ12345678
1660120240
2606120360
3601206120
412024030024
5
6
7
8
Sheet2
TAZ1234jTarget Pi78
1550100200355400
2505100300455460
3501005100255400
410020025020570702
i20535545562016351962
6
7
8
TAZ12345678
1660120240
2606120360
3601206120
412024030024
5
6
7
8
Sheet3
Sheet1
TAZProductionsTAZAttractionsTAZ12345678
112191550100200
2192122505100300
335343501005100
44438410020025020
555455
610666
713747
822828
120120
TAZ12345678
1660120240
2606120360
3601206120
412024030024
5
6
7
8
Sheet2
TAZ1234jTarget Oi78
1550100200355400
2505100300455460
3501005100255400
410020025020570702
i20535545562016351962
6
7
8
TAZ12345678
1660120240
2606120360
3601206120
412024030024
5
6
7
8
Sheet3
Sheet1
TAZProductionsTAZAttractionsTAZ12345678
112191550100200
2192122505100300
335343501005100
44438410020025020
555455
610666
713747
822828
120120
TAZ12345678
1660120240
2606120360
3601206120
412024030024
5
6
7
8
Sheet2
TAZ1234jTarget Oi78
1550100200355400
2505100300455460
3501005100255400
410020025020570702
i20535545562016351962
6
7
8
TAZ12345678
1660120240
2606120360
3601206120
412024030024
5
6
7
8
Sheet3
Sheet1
TAZProductionsTAZAttractionsTAZ12345678
112191550100200
2192122505100300
335343501005100
44438410020025020
555455
610666
713747
822828
120120
TAZ12345678
1660120240
2606120360
3601206120
412024030024
5
6
7
8
Sheet2
TAZ1234jTarget Oi78
1550100200355400
2505100300455460
3501005100255400
410020025020570702
i20535545562016351962
6
7
8
TAZ12345678
1660120240
2606120360
3601206120
412024030024
5
6
7
8
Sheet3
Singly-Constrained Growth Factor Method Tij = tij (Target Pi) / (j) = 5 (400 / 355)= 5.6
Sheet1
TAZProductionsTAZAttractionsTAZ12345678
112191550100200
2192122505100300
335343501005100
44438410020025020
555455
610666
713747
822828
120120
TAZ12345678
1660120240
2606120360
3601206120
412024030024
5
6
7
8
Sheet2
TAZ1234jTarget Pi78
1550100200355400
2505100300455460
3501005100255400
410020025020570702
i20535545562016351962
6
7
8
TAZ12345678
1660120240
2606120360
3601206120
412024030024
5
6
7
8
Sheet3
Singly-Constrained Growth Factor MethodCan also perform the singly-constrained growth factor method for a destination specific future trip tableBy multiplying each column by the ratio of (Target Aj) / (i)
Sheet1
TAZProductionsTAZAttractionsTAZ12345678
112191550100200
2192122505100300
335343501005100
44438410020025020
555455
610666
713747
822828
120120
TAZ12345678
1660120240
2606120360
3601206120
412024030024
5
6
7
8
Sheet2
TAZ1234jTarget Oi78
1550100200355400
2505100300455460
3501005100255400
410020025020570702
i20535545562016351962
6
7
8
TAZ12345678
1660120240
2606120360
3601206120
412024030024
5
6
7
8
TAZ1234jTarget Oi78
15.656.3112.7225.4400400
250.55.1101.1303.3460460
378.4156.97.8156.9400400
4123.2246.3307.924.6702702
i257.7464.6529.5710.219621962
6
7
8
Sheet3
TAZ1234jTarget Oi78
1550100200355400
2505100300455460
3501005100255400
410020025020570702
i20535545562016351962
Target Aj1804063807401706
7
8
TAZ12345678
1660120240
2606120360
3601206120
412024030024
5
6
7
8
TAZ1234jTarget Oi78
15.656.3112.7225.4400400
250.55.1101.1303.3460460
378.4156.97.8156.9400400
4123.2246.3307.924.6702702
i257.7464.6529.5710.219621962
6
7
8
Overview of the Singly-Constrained Growth Factor MethodologyOne of the simplest trip distribution techniquesUsed with existing trip table & future trip endsTypically, we balance flows after processingThis means that the total number of productions equals the total number of attractions (or in terms of origins & destinations)Tij = TjiBut there are more advanced growth factor models
Average Growth Factor Model
Average Growth Factor Function F = Growth Factor =Ratio of Target Trips toPrevious Iteration Trips k =Iteration Numberg ( )=Fik FjkF.kg ( )=Fik + Fjk2
The Basic StepsCollect InputsMatrix of Existing Trips, {tij}Vector of Future Trips Ends, {Ti}Compute Growth Factor for each zone
Compute Inter-zonal Flows
Compute Trips Ends
If tik = Ti for each zone i, then stop otherwise, go back to Step 1>Fik=Titik-1=Target Trip EndPrevious Iteration Trip End>tijk = tijk-1 [g(Fik, Fjk, )] for each ij pairtik = tijk for each zone i
Growth Factor Models: Average Factor Example
SC Growth Model HW
Singly-constrained by Originating
1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0
106027557190612001.32
250041044390310501.16
3123610472313801.65
42052657505457701.41
3783867601061
1234
10793637541196
25804765141047
3203101078381
42893741060768
550553.5944.351345.15
Singly-constrained by Destined
1234T(i)0T(i)^
10602755719061200
25004104439031050
312361047231380
4205265750545770
T(i)03783867601061
T(i)^670730950995
F(i)1 = T(i)^ / T(i)01.771.891.250.94
1234
10113344537994
28905134161017
3218115044377
4363501940957
669730950997
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
Average Factors HW
Observed Trips Tij(0)
1234Ti(0)Ti^Fi(1) = Ti^ / Ti(0)
106027557190612001.32
250041044390310501.16
3123610472313801.65
42052657505457701.41
Tj(0)3783867601061
Tj^670730950995
Fj(1) = Tj^ / Tj(0)1.771.891.250.94
Iteration 1: Fij(1) = [Fi(1) + Fj(1)] / 2
1234
11.5461.6061.2851.129
21.4661.5261.2051.049
31.7111.7711.4501.294
41.5911.6511.3301.174
tij(1) = tij(0) * Fij(1)
1234ti(1)TiFi(2) = Ti / ti(1)
10.0096.34353.38644.60109412001.10
273.310.00494.05464.66103210501.02
3210.48108.010.0060.813793801.00
4326.20437.4199.750.008637700.89
tj(1)6106429471170
Tj670730950995
Fj(2) = Tj / tj(1)1.101.141.000.85
Iteration 2: Fij(2) = [Fi(2) + Fj(2)] / 2
1234
11.0991.1191.0510.975
21.0591.0791.0110.935
31.0491.0691.0010.925
40.9941.0140.9460.870
Tij(2) = Tij(1) * Fij(2)
1234Ti(2)Ti^Fi(3) = Ti^ / Ti(2)
10.00107.78371.57628.61110812001.08
277.650.00499.73434.55101210501.04
3220.83115.430.0056.263933800.97
4324.31443.4394.410.008627700.89
Tj(2)6236679661119
Tj^670730950995
Fj(2) = Tj^ / Tj(1)1.081.100.980.89
Iteration 3: Fij(3) = [Fi(3) + Fj(3)] / 2
1234
11.0781.0881.0320.984
21.0581.0681.0120.964
31.0231.0330.9770.929
40.9830.9930.9370.889
Tij(3) = Tij(2) * Fij(3)
1234Ti(3)Ti^Fi(4) = Ti^ / Ti(3)
10.00117.21383.41618.82111912001.07
282.150.00505.66419.09100710501.04
3225.89119.190.0052.293973800.96
4318.76440.1188.450.008477700.91
Tj(3)6276779781090
Tj^670730950995
Fj(4) = Tj^ / Tj(3)1.071.080.970.91
Iteration 4: Fij(4) = [Fi(4) + Fj(4)] / 2
1234
11.0691.0751.0210.991
21.0541.0601.0060.976
31.0141.0200.9660.936
40.9890.9950.9410.911
Tij(4) = Tij(3) * Fij(4)
1234Ti(4)Ti^Fi(5) = Ti^ / Ti(4)
10.00125.95391.43613.46113112001.06
286.620.00508.65409.17100410501.05
3229.16121.520.0048.964003800.95
4315.40437.7183.230.008367700.92
Tj(4)6316859831072
Tj^670730950995
Fj(5) = Tj^ / Tj(4)1.061.070.970.93
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
DETROIT FACTORS HW
Observed Trips T(ij)0
1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0
10251020551152.09
225060301151501.30
31060015851351.59
4203015065951.46
sum =3204951.55= F(.)1
Iteration 1: F(ij)1 = [F(i)1 * F(j)1] / F(.)1
1234
12.8181.7532.1441.969
21.7531.0901.3341.225
32.1441.3341.6311.498
41.9691.2251.4981.375
T(ij)1 = T(ij)0 * F(ij)1
1234T(i)1T(i)^F(i)2 = T(i)^ / T(i)1
104421391051151.10
244080371611500.93
321800221241351.09
4393722099950.96
sum =4884951.01= F(.)2
Iteration 2: F(ij)2 = [F(i)2 * F(j)2] / F(.)2
1234
11.1981.0131.1871.046
21.0130.8561.0040.884
31.1871.0041.1761.036
41.0460.8841.0360.912
T(ij)2 = T(ij)1 * F(ij)2
1234T(i)2T(i)^F(i)3 = T(i)^ / T(i)2
104425411111151.04
244080321571500.95
325800231291351.05
4413223097950.98
sum =4944951.00= F(.)3
Iteration 3: F(ij)3 = [F(i)3 * F(j)3] / F(.)3
1234
11.0820.9881.0921.019
20.9880.9030.9980.931
31.0920.9981.1031.029
41.0190.9311.0290.960
T(ij)3 = T(ij)2 * F(ij)3
1234T(i)3T(i)^F(i)4 = T(i)^ / T(i)3
104428421141151.01
244080301541500.97
328800241321351.02
4423024096950.99
sum =4964951.00= F(.)4
Iteration 4: F(ij)4 = [F(i)4 * F(j)4] / F(.)4
1234
11.0200.9801.0301.000
20.9800.9410.9890.960
31.0300.9891.0401.010
41.0000.9601.0100.980
T(ij)4 = T(ij)3 * F(ij)4
1234T(i)4T(i)^F(i)5 = T(i)^ / T(i)4
104329421141151.01
243079291511500.99
329790241321351.02
4422924095951.00
sum =492495
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
FRATAR METHOD HW
Observed Trips T(ij)0
1234T(i)0T(i)^F(i)1Sum(z) T(iz)0 F(z)1
10251020551152.0978
225060301151501.30191
31060015851351.59121
4203015065951.46105
Iteration 1: t(ij)1 = T(ij)0 T(i)^ F(j)1 / Sum(z) {T(iz)0 F(z)1]
1234
10482443
24107534
32387024
43835220
T(ij)1 = [t(ij)1 + t(ji)1] / 2
1234T(i)1T(i)^F(i)2Sum(z) T(iz)1 F(z)2
104523411091151.06106
245081351601500.94167
323810231271351.06123
4413523099950.96100
Iteration 2: t(ij)2 = T(ij)1 T(i)^ F(j)2 / Sum(z) {T(iz)1 F(z)2]
1234
10462742
24307730
32783024
44131230
T(ij)2 = [t(ij)2 + t(ji)2] / 2
1234T(i)2T(i)^F(i)3Sum(z) T(iz)2 F(z)3
104427421131151.02112
244080311551500.97158
327800241311351.03129
4423124096950.9997
Iteration 3: t(ij)3 = T(ij)2 T(i)^ F(j)3 / Sum(z) {T(iz)2 F(z)3]
1234
10442942
24307929
32981025
44229240
T(ij)3 = [t(ij)3 + t(ji)3] / 2
1234T(i)3T(i)^F(i)4
104329421141151.01
243080291521500.98
329800241331351.01
4422924095951.00
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
SC Growth Model HW
Singly-constrained by Originating
1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0
106027557190612001.32
250041044390310501.16
3123610472313801.65
42052657505457701.41
3783867601061
1234
10793637541196
25804765141047
3203101078381
42893741060768
550553.5944.351345.15
Singly-constrained by Destined
1234T(i)0T(i)^
10602755719061200
25004104439031050
312361047231380
4205265750545770
T(i)03783867601061
T(i)^670730950995
F(i)1 = T(i)^ / T(i)01.771.891.250.94
1234
10113344537994
28905134161017
3218115044377
4363501940957
669730950997
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
Average Factors HW
Observed Trips Tij(0)
1234Ti(0)Ti^Fi(1) = Ti^ / Ti(0)
106027557190612001.32
250041044390310501.16
3123610472313801.65
42052657505457701.41
Tj(0)3783867601061
Tj^670730950995
Fj(1) = Tj^ / Tj(0)1.771.891.250.94
Iteration 1: Fij(1) = [Fi(1) + Fj(1)] / 2
1234
11.5461.6061.2851.129
21.4661.5261.2051.049
31.7111.7711.4501.294
41.5911.6511.3301.174
tij(1) = tij(0) * Fij(1)
1234ti(1)TiFi(2) = Ti / ti(1)
10.0096.34353.38644.60109412001.10
273.310.00494.05464.66103210501.02
3210.48108.010.0060.813793801.00
4326.20437.4199.750.008637700.89
tj(1)6106429471170
Tj670730950995
Fj(2) = Tj / tj(1)1.101.141.000.85
Iteration 2: Fij(2) = [Fi(2) + Fj(2)] / 2
1234
11.0991.1191.0510.975
21.0591.0791.0110.935
31.0491.0691.0010.925
40.9941.0140.9460.870
Tij(2) = Tij(1) * Fij(2)
1234Ti(2)Ti^Fi(3) = Ti^ / Ti(2)
10.00107.78371.57628.61110812001.08
277.650.00499.73434.55101210501.04
3220.83115.430.0056.263933800.97
4324.31443.4394.410.008627700.89
Tj(2)6236679661119
Tj^670730950995
Fj(2) = Tj^ / Tj(1)1.081.100.980.89
Iteration 3: Fij(3) = [Fi(3) + Fj(3)] / 2
1234
11.0781.0881.0320.984
21.0581.0681.0120.964
31.0231.0330.9770.929
40.9830.9930.9370.889
Tij(3) = Tij(2) * Fij(3)
1234Ti(3)Ti^Fi(4) = Ti^ / Ti(3)
10.00117.21383.41618.82111912001.07
282.150.00505.66419.09100710501.04
3225.89119.190.0052.293973800.96
4318.76440.1188.450.008477700.91
Tj(3)6276779781090
Tj^670730950995
Fj(4) = Tj^ / Tj(3)1.071.080.970.91
Iteration 4: Fij(4) = [Fi(4) + Fj(4)] / 2
1234
11.0691.0751.0210.991
21.0541.0601.0060.976
31.0141.0200.9660.936
40.9890.9950.9410.911
Tij(4) = Tij(3) * Fij(4)
1234Ti(4)Ti^Fi(5) = Ti^ / Ti(4)
10.00125.95391.43613.46113112001.06
286.620.00508.65409.17100410501.05
3229.16121.520.0048.964003800.95
4315.40437.7183.230.008367700.92
Tj(4)6316859831072
Tj^670730950995
Fj(5) = Tj^ / Tj(4)1.061.070.970.93
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
DETROIT FACTORS HW
Observed Trips T(ij)0
1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0
10251020551152.09
225060301151501.30
31060015851351.59
4203015065951.46
sum =3204951.55= F(.)1
Iteration 1: F(ij)1 = [F(i)1 * F(j)1] / F(.)1
1234
12.8181.7532.1441.969
21.7531.0901.3341.225
32.1441.3341.6311.498
41.9691.2251.4981.375
T(ij)1 = T(ij)0 * F(ij)1
1234T(i)1T(i)^F(i)2 = T(i)^ / T(i)1
104421391051151.10
244080371611500.93
321800221241351.09
4393722099950.96
sum =4884951.01= F(.)2
Iteration 2: F(ij)2 = [F(i)2 * F(j)2] / F(.)2
1234
11.1981.0131.1871.046
21.0130.8561.0040.884
31.1871.0041.1761.036
41.0460.8841.0360.912
T(ij)2 = T(ij)1 * F(ij)2
1234T(i)2T(i)^F(i)3 = T(i)^ / T(i)2
104425411111151.04
244080321571500.95
325800231291351.05
4413223097950.98
sum =4944951.00= F(.)3
Iteration 3: F(ij)3 = [F(i)3 * F(j)3] / F(.)3
1234
11.0820.9881.0921.019
20.9880.9030.9980.931
31.0920.9981.1031.029
41.0190.9311.0290.960
T(ij)3 = T(ij)2 * F(ij)3
1234T(i)3T(i)^F(i)4 = T(i)^ / T(i)3
104428421141151.01
244080301541500.97
328800241321351.02
4423024096950.99
sum =4964951.00= F(.)4
Iteration 4: F(ij)4 = [F(i)4 * F(j)4] / F(.)4
1234
11.0200.9801.0301.000
20.9800.9410.9890.960
31.0300.9891.0401.010
41.0000.9601.0100.980
T(ij)4 = T(ij)3 * F(ij)4
1234T(i)4T(i)^F(i)5 = T(i)^ / T(i)4
104329421141151.01
243079291511500.99
329790241321351.02
4422924095951.00
sum =492495
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
FRATAR METHOD HW
Observed Trips T(ij)0
1234T(i)0T(i)^F(i)1Sum(z) T(iz)0 F(z)1
10251020551152.0978
225060301151501.30191
31060015851351.59121
4203015065951.46105
Iteration 1: t(ij)1 = T(ij)0 T(i)^ F(j)1 / Sum(z) {T(iz)0 F(z)1]
1234
10482443
24107534
32387024
43835220
T(ij)1 = [t(ij)1 + t(ji)1] / 2
1234T(i)1T(i)^F(i)2Sum(z) T(iz)1 F(z)2
104523411091151.06106
245081351601500.94167
323810231271351.06123
4413523099950.96100
Iteration 2: t(ij)2 = T(ij)1 T(i)^ F(j)2 / Sum(z) {T(iz)1 F(z)2]
1234
10462742
24307730
32783024
44131230
T(ij)2 = [t(ij)2 + t(ji)2] / 2
1234T(i)2T(i)^F(i)3Sum(z) T(iz)2 F(z)3
104427421131151.02112
244080311551500.97158
327800241311351.03129
4423124096950.9997
Iteration 3: t(ij)3 = T(ij)2 T(i)^ F(j)3 / Sum(z) {T(iz)2 F(z)3]
1234
10442942
24307929
32981025
44229240
T(ij)3 = [t(ij)3 + t(ji)3] / 2
1234T(i)3T(i)^F(i)4
104329421141151.01
243080291521500.98
329800241331351.01
4422924095951.00
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
SC Growth Model HW
Singly-constrained by Originating
1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0
106027557190612001.32
250041044390310501.16
3123610472313801.65
42052657505457701.41
3783867601061
1234
10793637541196
25804765141047
3203101078381
42893741060768
550553.5944.351345.15
Singly-constrained by Destined
1234T(i)0T(i)^
10602755719061200
25004104439031050
312361047231380
4205265750545770
T(i)03783867601061
T(i)^670730950995
F(i)1 = T(i)^ / T(i)01.771.891.250.94
1234
10113344537994
28905134161017
3218115044377
4363501940957
669730950997
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
Average Factors HW
Observed Trips Tij(0)
1234Ti(0)Ti^Fi(1) = Ti^ / Ti(0)
106027557190612001.32
250041044390310501.16
3123610472313801.65
42052657505457701.41
Tj(0)3783867601061
Tj^670730950995
Fj(1) = Tj^ / Tj(0)1.771.891.250.94
Iteration 1: Fij(1) = [Fi(1) + Fj(1)] / 2
1234
11.5461.6061.2851.129
21.4661.5261.2051.049
31.7111.7711.4501.294
41.5911.6511.3301.174
Tij(1) = Tij(0) * Fij(1)
1234ti(1)TiFi(2) = Ti / ti(1)
10.0096.34353.38644.60109412001.10
273.310.00494.05464.66103210501.02
3210.48108.010.0060.813793801.00
4326.20437.4199.750.008637700.89
tj(1)6106429471170
Tj670730950995
Fj(2) = Tj / tj(1)1.101.141.000.85
Iteration 2: Fij(2) = [Fi(2) + Fj(2)] / 2
1234
11.0991.1191.0510.975
21.0591.0791.0110.935
31.0491.0691.0010.925
40.9941.0140.9460.870
Tij(2) = Tij(1) * Fij(2)
1234Ti(2)Ti^Fi(3) = Ti^ / Ti(2)
10.00107.78371.57628.61110812001.08
277.650.00499.73434.55101210501.04
3220.83115.430.0056.263933800.97
4324.31443.4394.410.008627700.89
Tj(2)6236679661119
Tj^670730950995
Fj(2) = Tj^ / Tj(1)1.081.100.980.89
Iteration 3: Fij(3) = [Fi(3) + Fj(3)] / 2
1234
11.0781.0881.0320.984
21.0581.0681.0120.964
31.0231.0330.9770.929
40.9830.9930.9370.889
Tij(3) = Tij(2) * Fij(3)
1234Ti(3)Ti^Fi(4) = Ti^ / Ti(3)
10.00117.21383.41618.82111912001.07
282.150.00505.66419.09100710501.04
3225.89119.190.0052.293973800.96
4318.76440.1188.450.008477700.91
Tj(3)6276779781090
Tj^670730950995
Fj(4) = Tj^ / Tj(3)1.071.080.970.91
Iteration 4: Fij(4) = [Fi(4) + Fj(4)] / 2
1234
11.0691.0751.0210.991
21.0541.0601.0060.976
31.0141.0200.9660.936
40.9890.9950.9410.911
Tij(4) = Tij(3) * Fij(4)
1234Ti(4)Ti^Fi(5) = Ti^ / Ti(4)
10.00125.95391.43613.46113112001.06
286.620.00508.65409.17100410501.05
3229.16121.520.0048.964003800.95
4315.40437.7183.230.008367700.92
Tj(4)6316859831072
Tj^670730950995
Fj(5) = Tj^ / Tj(4)1.061.070.970.93
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
DETROIT FACTORS HW
Observed Trips T(ij)0
1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0
10251020551152.09
225060301151501.30
31060015851351.59
4203015065951.46
sum =3204951.55= F(.)1
Iteration 1: F(ij)1 = [F(i)1 * F(j)1] / F(.)1
1234
12.8181.7532.1441.969
21.7531.0901.3341.225
32.1441.3341.6311.498
41.9691.2251.4981.375
T(ij)1 = T(ij)0 * F(ij)1
1234T(i)1T(i)^F(i)2 = T(i)^ / T(i)1
104421391051151.10
244080371611500.93
321800221241351.09
4393722099950.96
sum =4884951.01= F(.)2
Iteration 2: F(ij)2 = [F(i)2 * F(j)2] / F(.)2
1234
11.1981.0131.1871.046
21.0130.8561.0040.884
31.1871.0041.1761.036
41.0460.8841.0360.912
T(ij)2 = T(ij)1 * F(ij)2
1234T(i)2T(i)^F(i)3 = T(i)^ / T(i)2
104425411111151.04
244080321571500.95
325800231291351.05
4413223097950.98
sum =4944951.00= F(.)3
Iteration 3: F(ij)3 = [F(i)3 * F(j)3] / F(.)3
1234
11.0820.9881.0921.019
20.9880.9030.9980.931
31.0920.9981.1031.029
41.0190.9311.0290.960
T(ij)3 = T(ij)2 * F(ij)3
1234T(i)3T(i)^F(i)4 = T(i)^ / T(i)3
104428421141151.01
244080301541500.97
328800241321351.02
4423024096950.99
sum =4964951.00= F(.)4
Iteration 4: F(ij)4 = [F(i)4 * F(j)4] / F(.)4
1234
11.0200.9801.0301.000
20.9800.9410.9890.960
31.0300.9891.0401.010
41.0000.9601.0100.980
T(ij)4 = T(ij)3 * F(ij)4
1234T(i)4T(i)^F(i)5 = T(i)^ / T(i)4
104329421141151.01
243079291511500.99
329790241321351.02
4422924095951.00
sum =492495
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
FRATAR METHOD HW
Observed Trips T(ij)0
1234T(i)0T(i)^F(i)1Sum(z) T(iz)0 F(z)1
10251020551152.0978
225060301151501.30191
31060015851351.59121
4203015065951.46105
Iteration 1: t(ij)1 = T(ij)0 T(i)^ F(j)1 / Sum(z) {T(iz)0 F(z)1]
1234
10482443
24107534
32387024
43835220
T(ij)1 = [t(ij)1 + t(ji)1] / 2
1234T(i)1T(i)^F(i)2Sum(z) T(iz)1 F(z)2
104523411091151.06106
245081351601500.94167
323810231271351.06123
4413523099950.96100
Iteration 2: t(ij)2 = T(ij)1 T(i)^ F(j)2 / Sum(z) {T(iz)1 F(z)2]
1234
10462742
24307730
32783024
44131230
T(ij)2 = [t(ij)2 + t(ji)2] / 2
1234T(i)2T(i)^F(i)3Sum(z) T(iz)2 F(z)3
104427421131151.02112
244080311551500.97158
327800241311351.03129
4423124096950.9997
Iteration 3: t(ij)3 = T(ij)2 T(i)^ F(j)3 / Sum(z) {T(iz)2 F(z)3]
1234
10442942
24307929
32981025
44229240
T(ij)3 = [t(ij)3 + t(ji)3] / 2
1234T(i)3T(i)^F(i)4
104329421141151.01
243080291521500.98
329800241331351.01
4422924095951.00
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
SC Growth Model HW
Singly-constrained by Originating
1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0
106027557190612001.32
250041044390310501.16
3123610472313801.65
42052657505457701.41
3783867601061
1234
10793637541196
25804765141047
3203101078381
42893741060768
550553.5944.351345.15
Singly-constrained by Destined
1234T(i)0T(i)^
10602755719061200
25004104439031050
312361047231380
4205265750545770
T(i)03783867601061
T(i)^670730950995
F(i)1 = T(i)^ / T(i)01.771.891.250.94
1234
10113344537994
28905134161017
3218115044377
4363501940957
669730950997
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
Average Factors HW
Observed Trips Tij(0)
1234Ti(0)Ti^Fi(1) = Ti^ / Ti(0)
106027557190612001.32
250041044390310501.16
3123610472313801.65
42052657505457701.41
Tj(0)3783867601061
Tj^670730950995
Fj(1) = Tj^ / Tj(0)1.771.891.250.94
Iteration 1: Fij(1) = [Fi(1) + Fj(1)] / 2
1234
11.5461.6061.2851.129
21.4661.5261.2051.049
31.7111.7711.4501.294
41.5911.6511.3301.174
tij(1) = tij(0) * Fij(1)
1234ti(1)TiFi(2) = Ti / ti(1)
10.0096.34353.38644.60109412001.10
273.310.00494.05464.66103210501.02
3210.48108.010.0060.813793801.00
4326.20437.4199.750.008637700.89
tj(1)6106429471170
Tj670730950995
Fj(2) = Tj / tj(1)1.101.141.000.85
Iteration 2: Fij(2) = [Fi(2) + Fj(2)] / 2
1234
11.0991.1191.0510.975
21.0591.0791.0110.935
31.0491.0691.0010.925
40.9941.0140.9460.870
Tij(2) = Tij(1) * Fij(2)
1234Ti(2)Ti^Fi(3) = Ti^ / Ti(2)
10.00107.78371.57628.61110812001.08
277.650.00499.73434.55101210501.04
3220.83115.430.0056.263933800.97
4324.31443.4394.410.008627700.89
Tj(2)6236679661119
Tj^670730950995
Fj(2) = Tj^ / Tj(1)1.081.100.980.89
Iteration 3: Fij(3) = [Fi(3) + Fj(3)] / 2
1234
11.0781.0881.0320.984
21.0581.0681.0120.964
31.0231.0330.9770.929
40.9830.9930.9370.889
Tij(3) = Tij(2) * Fij(3)
1234Ti(3)Ti^Fi(4) = Ti^ / Ti(3)
10.00117.21383.41618.82111912001.07
282.150.00505.66419.09100710501.04
3225.89119.190.0052.293973800.96
4318.76440.1188.450.008477700.91
Tj(3)6276779781090
Tj^670730950995
Fj(4) = Tj^ / Tj(3)1.071.080.970.91
Iteration 4: Fij(4) = [Fi(4) + Fj(4)] / 2
1234
11.0691.0751.0210.991
21.0541.0601.0060.976
31.0141.0200.9660.936
40.9890.9950.9410.911
Tij(4) = Tij(3) * Fij(4)
1234Ti(4)Ti^Fi(5) = Ti^ / Ti(4)
10.00125.95391.43613.46113112001.06
286.620.00508.65409.17100410501.05
3229.16121.520.0048.964003800.95
4315.40437.7183.230.008367700.92
Tj(4)6316859831072
Tj^670730950995
Fj(5) = Tj^ / Tj(4)1.061.070.970.93
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
DETROIT FACTORS HW
Observed Trips T(ij)0
1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0
10251020551152.09
225060301151501.30
31060015851351.59
4203015065951.46
sum =3204951.55= F(.)1
Iteration 1: F(ij)1 = [F(i)1 * F(j)1] / F(.)1
1234
12.8181.7532.1441.969
21.7531.0901.3341.225
32.1441.3341.6311.498
41.9691.2251.4981.375
T(ij)1 = T(ij)0 * F(ij)1
1234T(i)1T(i)^F(i)2 = T(i)^ / T(i)1
104421391051151.10
244080371611500.93
321800221241351.09
4393722099950.96
sum =4884951.01= F(.)2
Iteration 2: F(ij)2 = [F(i)2 * F(j)2] / F(.)2
1234
11.1981.0131.1871.046
21.0130.8561.0040.884
31.1871.0041.1761.036
41.0460.8841.0360.912
T(ij)2 = T(ij)1 * F(ij)2
1234T(i)2T(i)^F(i)3 = T(i)^ / T(i)2
104425411111151.04
244080321571500.95
325800231291351.05
4413223097950.98
sum =4944951.00= F(.)3
Iteration 3: F(ij)3 = [F(i)3 * F(j)3] / F(.)3
1234
11.0820.9881.0921.019
20.9880.9030.9980.931
31.0920.9981.1031.029
41.0190.9311.0290.960
T(ij)3 = T(ij)2 * F(ij)3
1234T(i)3T(i)^F(i)4 = T(i)^ / T(i)3
104428421141151.01
244080301541500.97
328800241321351.02
4423024096950.99
sum =4964951.00= F(.)4
Iteration 4: F(ij)4 = [F(i)4 * F(j)4] / F(.)4
1234
11.0200.9801.0301.000
20.9800.9410.9890.960
31.0300.9891.0401.010
41.0000.9601.0100.980
T(ij)4 = T(ij)3 * F(ij)4
1234T(i)4T(i)^F(i)5 = T(i)^ / T(i)4
104329421141151.01
243079291511500.99
329790241321351.02
4422924095951.00
sum =492495
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
FRATAR METHOD HW
Observed Trips T(ij)0
1234T(i)0T(i)^F(i)1Sum(z) T(iz)0 F(z)1
10251020551152.0978
225060301151501.30191
31060015851351.59121
4203015065951.46105
Iteration 1: t(ij)1 = T(ij)0 T(i)^ F(j)1 / Sum(z) {T(iz)0 F(z)1]
1234
10482443
24107534
32387024
43835220
T(ij)1 = [t(ij)1 + t(ji)1] / 2
1234T(i)1T(i)^F(i)2Sum(z) T(iz)1 F(z)2
104523411091151.06106
245081351601500.94167
323810231271351.06123
4413523099950.96100
Iteration 2: t(ij)2 = T(ij)1 T(i)^ F(j)2 / Sum(z) {T(iz)1 F(z)2]
1234
10462742
24307730
32783024
44131230
T(ij)2 = [t(ij)2 + t(ji)2] / 2
1234T(i)2T(i)^F(i)3Sum(z) T(iz)2 F(z)3
104427421131151.02112
244080311551500.97158
327800241311351.03129
4423124096950.9997
Iteration 3: t(ij)3 = T(ij)2 T(i)^ F(j)3 / Sum(z) {T(iz)2 F(z)3]
1234
10442942
24307929
32981025
44229240
T(ij)3 = [t(ij)3 + t(ji)3] / 2
1234T(i)3T(i)^F(i)4
104329421141151.01
243080291521500.98
329800241331351.01
4422924095951.00
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
SC Growth Model HW
Singly-constrained by Originating
1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0
106027557190612001.32
250041044390310501.16
3123610472313801.65
42052657505457701.41
3783867601061
1234
10793637541196
25804765141047
3203101078381
42893741060768
550553.5944.351345.15
Singly-constrained by Destined
1234T(i)0T(i)^
10602755719061200
25004104439031050
312361047231380
4205265750545770
T(i)03783867601061
T(i)^670730950995
F(i)1 = T(i)^ / T(i)01.771.891.250.94
1234
10113344537994
28905134161017
3218115044377
4363501940957
669730950997
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
Average Factors HW
Observed Trips Tij(0)
1234Ti(0)Ti^Fi(1) = Ti^ / Ti(0)
106027557190612001.32
250041044390310501.16
3123610472313801.65
42052657505457701.41
Tj(0)3783867601061
Tj^670730950995
Fj(1) = Tj^ / Tj(0)1.771.891.250.94
Iteration 1: Fij(1) = [Fi(1) + Fj(1)] / 2
1234
11.5461.6061.2851.129
21.4661.5261.2051.049
31.7111.7711.4501.294
41.5911.6511.3301.174
tij(1) = tij(0) * Fij(1)
1234ti(1)TiFi(2) = Ti / ti(1)
10.0096.34353.38644.60109412001.10
273.310.00494.05464.66103210501.02
3210.48108.010.0060.813793801.00
4326.20437.4199.750.008637700.89
tj(1)6106429471170
Tj670730950995
Fj(2) = Tj / tj(1)1.101.141.000.85
Iteration 2: Fij(2) = [Fi(2) + Fj(2)] / 2
1234
11.0991.1191.0510.975
21.0591.0791.0110.935
31.0491.0691.0010.925
40.9941.0140.9460.870
Tij(2) = Tij(1) * Fij(2)
1234Ti(2)Ti^Fi(3) = Ti^ / Ti(2)
10.00107.78371.57628.61110812001.08
277.650.00499.73434.55101210501.04
3220.83115.430.0056.263933800.97
4324.31443.4394.410.008627700.89
Tj(2)6236679661119
Tj^670730950995
Fj(2) = Tj^ / Tj(1)1.081.100.980.89
Iteration 3: Fij(3) = [Fi(3) + Fj(3)] / 2
1234
11.0781.0881.0320.984
21.0581.0681.0120.964
31.0231.0330.9770.929
40.9830.9930.9370.889
Tij(3) = Tij(2) * Fij(3)
1234Ti(3)Ti^Fi(4) = Ti^ / Ti(3)
10.00117.21383.41618.82111912001.07
282.150.00505.66419.09100710501.04
3225.89119.190.0052.293973800.96
4318.76440.1188.450.008477700.91
Tj(3)6276779781090
Tj^670730950995
Fj(4) = Tj^ / Tj(3)1.071.080.970.91
Iteration 4: Fij(4) = [Fi(4) + Fj(4)] / 2
1234
11.0691.0751.0210.991
21.0541.0601.0060.976
31.0141.0200.9660.936
40.9890.9950.9410.911
Tij(4) = Tij(3) * Fij(4)
1234Ti(4)Ti^Fi(5) = Ti^ / Ti(4)
10.00125.95391.43613.46113112001.06
286.620.00508.65409.17100410501.05
3229.16121.520.0048.964003800.95
4315.40437.7183.230.008367700.92
Tj(4)6316859831072
Tj^670730950995
Fj(5) = Tj^ / Tj(4)1.061.070.970.93
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
DETROIT FACTORS HW
Observed Trips T(ij)0
1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0
10251020551152.09
225060301151501.30
31060015851351.59
4203015065951.46
sum =3204951.55= F(.)1
Iteration 1: F(ij)1 = [F(i)1 * F(j)1] / F(.)1
1234
12.8181.7532.1441.969
21.7531.0901.3341.225
32.1441.3341.6311.498
41.9691.2251.4981.375
T(ij)1 = T(ij)0 * F(ij)1
1234T(i)1T(i)^F(i)2 = T(i)^ / T(i)1
104421391051151.10
244080371611500.93
321800221241351.09
4393722099950.96
sum =4884951.01= F(.)2
Iteration 2: F(ij)2 = [F(i)2 * F(j)2] / F(.)2
1234
11.1981.0131.1871.046
21.0130.8561.0040.884
31.1871.0041.1761.036
41.0460.8841.0360.912
T(ij)2 = T(ij)1 * F(ij)2
1234T(i)2T(i)^F(i)3 = T(i)^ / T(i)2
104425411111151.04
244080321571500.95
325800231291351.05
4413223097950.98
sum =4944951.00= F(.)3
Iteration 3: F(ij)3 = [F(i)3 * F(j)3] / F(.)3
1234
11.0820.9881.0921.019
20.9880.9030.9980.931
31.0920.9981.1031.029
41.0190.9311.0290.960
T(ij)3 = T(ij)2 * F(ij)3
1234T(i)3T(i)^F(i)4 = T(i)^ / T(i)3
104428421141151.01
244080301541500.97
328800241321351.02
4423024096950.99
sum =4964951.00= F(.)4
Iteration 4: F(ij)4 = [F(i)4 * F(j)4] / F(.)4
1234
11.0200.9801.0301.000
20.9800.9410.9890.960
31.0300.9891.0401.010
41.0000.9601.0100.980
T(ij)4 = T(ij)3 * F(ij)4
1234T(i)4T(i)^F(i)5 = T(i)^ / T(i)4
104329421141151.01
243079291511500.99
329790241321351.02
4422924095951.00
sum =492495
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
FRATAR METHOD HW
Observed Trips T(ij)0
1234T(i)0T(i)^F(i)1Sum(z) T(iz)0 F(z)1
10251020551152.0978
225060301151501.30191
31060015851351.59121
4203015065951.46105
Iteration 1: t(ij)1 = T(ij)0 T(i)^ F(j)1 / Sum(z) {T(iz)0 F(z)1]
1234
10482443
24107534
32387024
43835220
T(ij)1 = [t(ij)1 + t(ji)1] / 2
1234T(i)1T(i)^F(i)2Sum(z) T(iz)1 F(z)2
104523411091151.06106
245081351601500.94167
323810231271351.06123
4413523099950.96100
Iteration 2: t(ij)2 = T(ij)1 T(i)^ F(j)2 / Sum(z) {T(iz)1 F(z)2]
1234
10462742
24307730
32783024
44131230
T(ij)2 = [t(ij)2 + t(ji)2] / 2
1234T(i)2T(i)^F(i)3Sum(z) T(iz)2 F(z)3
104427421131151.02112
244080311551500.97158
327800241311351.03129
4423124096950.9997
Iteration 3: t(ij)3 = T(ij)2 T(i)^ F(j)3 / Sum(z) {T(iz)2 F(z)3]
1234
10442942
24307929
32981025
44229240
T(ij)3 = [t(ij)3 + t(ji)3] / 2
1234T(i)3T(i)^F(i)4
104329421141151.01
243080291521500.98
329800241331351.01
4422924095951.00
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
SC Growth Model HW
Singly-constrained by Originating
1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0
106027557190612001.32
250041044390310501.16
3123610472313801.65
42052657505457701.41
3783867601061
1234
10793637541196
25804765141047
3203101078381
42893741060768
550553.5944.351345.15
Singly-constrained by Destined
1234T(i)0T(i)^
10602755719061200
25004104439031050
312361047231380
4205265750545770
T(i)03783867601061
T(i)^670730950995
F(i)1 = T(i)^ / T(i)01.771.891.250.94
1234
10113344537994
28905134161017
3218115044377
4363501940957
669730950997
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
Average Factors HW
Observed Trips Tij(0)
1234Ti(0)Ti^Fi(1) = Ti^ / Ti(0)
106027557190612001.32
250041044390310501.16
3123610472313801.65
42052657505457701.41
Tj(0)3783867601061
Tj^670730950995
Fj(1) = Tj^ / Tj(0)1.771.891.250.94
Iteration 1: Fij(1) = [Fi(1) + Fj(1)] / 2
1234
11.5461.6061.2851.129
21.4661.5261.2051.049
31.7111.7711.4501.294
41.5911.6511.3301.174
tij(1) = tij(0) * Fij(1)
1234ti(1)TiFi(2) = Ti^ / Ti(1)
10.0096.34353.38644.60109412001.10
273.310.00494.05464.66103210501.02
3210.48108.010.0060.813793801.00
4326.20437.4199.750.008637700.89
tj(1)6106429471170
Tj670730950995
Fj(2) = Tj / tj(1)1.101.141.000.85
Iteration 2: Fij(2) = [Fi(2) + Fj(2)] / 2
1234
11.0991.1191.0510.975
21.0591.0791.0110.935
31.0491.0691.0010.925
40.9941.0140.9460.870
Tij(2) = Tij(1) * Fij(2)
1234Ti(2)Ti^Fi(3) = Ti^ / Ti(2)
10.00107.78371.57628.61110812001.08
277.650.00499.73434.55101210501.04
3220.83115.430.0056.263933800.97
4324.31443.4394.410.008627700.89
Tj(2)6236679661119
Tj^670730950995
Fj(2) = Tj^ / Tj(1)1.081.100.980.89
Iteration 3: Fij(3) = [Fi(3) + Fj(3)] / 2
1234
11.0781.0881.0320.984
21.0581.0681.0120.964
31.0231.0330.9770.929
40.9830.9930.9370.889
Tij(3) = Tij(2) * Fij(3)
1234Ti(3)Ti^Fi(4) = Ti^ / Ti(3)
10.00117.21383.41618.82111912001.07
282.150.00505.66419.09100710501.04
3225.89119.190.0052.293973800.96
4318.76440.1188.450.008477700.91
Tj(3)6276779781090
Tj^670730950995
Fj(4) = Tj^ / Tj(3)1.071.080.970.91
Iteration 4: Fij(4) = [Fi(4) + Fj(4)] / 2
1234
11.0691.0751.0210.991
21.0541.0601.0060.976
31.0141.0200.9660.936
40.9890.9950.9410.911
Tij(4) = Tij(3) * Fij(4)
1234Ti(4)Ti^Fi(5) = Ti^ / Ti(4)
10.00125.95391.43613.46113112001.06
286.620.00508.65409.17100410501.05
3229.16121.520.0048.964003800.95
4315.40437.7183.230.008367700.92
Tj(4)6316859831072
Tj^670730950995
Fj(5) = Tj^ / Tj(4)1.061.070.970.93
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
DETROIT FACTORS HW
Observed Trips T(ij)0
1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0
10251020551152.09
225060301151501.30
31060015851351.59
4203015065951.46
sum =3204951.55= F(.)1
Iteration 1: F(ij)1 = [F(i)1 * F(j)1] / F(.)1
1234
12.8181.7532.1441.969
21.7531.0901.3341.225
32.1441.3341.6311.498
41.9691.2251.4981.375
T(ij)1 = T(ij)0 * F(ij)1
1234T(i)1T(i)^F(i)2 = T(i)^ / T(i)1
104421391051151.10
244080371611500.93
321800221241351.09
4393722099950.96
sum =4884951.01= F(.)2
Iteration 2: F(ij)2 = [F(i)2 * F(j)2] / F(.)2
1234
11.1981.0131.1871.046
21.0130.8561.0040.884
31.1871.0041.1761.036
41.0460.8841.0360.912
T(ij)2 = T(ij)1 * F(ij)2
1234T(i)2T(i)^F(i)3 = T(i)^ / T(i)2
104425411111151.04
244080321571500.95
325800231291351.05
4413223097950.98
sum =4944951.00= F(.)3
Iteration 3: F(ij)3 = [F(i)3 * F(j)3] / F(.)3
1234
11.0820.9881.0921.019
20.9880.9030.9980.931
31.0920.9981.1031.029
41.0190.9311.0290.960
T(ij)3 = T(ij)2 * F(ij)3
1234T(i)3T(i)^F(i)4 = T(i)^ / T(i)3
104428421141151.01
244080301541500.97
328800241321351.02
4423024096950.99
sum =4964951.00= F(.)4
Iteration 4: F(ij)4 = [F(i)4 * F(j)4] / F(.)4
1234
11.0200.9801.0301.000
20.9800.9410.9890.960
31.0300.9891.0401.010
41.0000.9601.0100.980
T(ij)4 = T(ij)3 * F(ij)4
1234T(i)4T(i)^F(i)5 = T(i)^ / T(i)4
104329421141151.01
243079291511500.99
329790241321351.02
4422924095951.00
sum =492495
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
FRATAR METHOD HW
Observed Trips T(ij)0
1234T(i)0T(i)^F(i)1Sum(z) T(iz)0 F(z)1
10251020551152.0978
225060301151501.30191
31060015851351.59121
4203015065951.46105
Iteration 1: t(ij)1 = T(ij)0 T(i)^ F(j)1 / Sum(z) {T(iz)0 F(z)1]
1234
10482443
24107534
32387024
43835220
T(ij)1 = [t(ij)1 + t(ji)1] / 2
1234T(i)1T(i)^F(i)2Sum(z) T(iz)1 F(z)2
104523411091151.06106
245081351601500.94167
323810231271351.06123
4413523099950.96100
Iteration 2: t(ij)2 = T(ij)1 T(i)^ F(j)2 / Sum(z) {T(iz)1 F(z)2]
1234
10462742
24307730
32783024
44131230
T(ij)2 = [t(ij)2 + t(ji)2] / 2
1234T(i)2T(i)^F(i)3Sum(z) T(iz)2 F(z)3
104427421131151.02112
244080311551500.97158
327800241311351.03129
4423124096950.9997
Iteration 3: t(ij)3 = T(ij)2 T(i)^ F(j)3 / Sum(z) {T(iz)2 F(z)3]
1234
10442942
24307929
32981025
44229240
T(ij)3 = [t(ij)3 + t(ji)3] / 2
1234T(i)3T(i)^F(i)4
104329421141151.01
243080291521500.98
329800241331351.01
4422924095951.00
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
SC Growth Model HW
Singly-constrained by Originating
1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0
106027557190612001.32
250041044390310501.16
3123610472313801.65
42052657505457701.41
3783867601061
1234
10793637541196
25804765141047
3203101078381
42893741060768
550553.5944.351345.15
Singly-constrained by Destined
1234T(i)0T(i)^
10602755719061200
25004104439031050
312361047231380
4205265750545770
T(i)03783867601061
T(i)^670730950995
F(i)1 = T(i)^ / T(i)01.771.891.250.94
1234
10113344537994
28905134161017
3218115044377
4363501940957
669730950997
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
Average Factors HW
1234
106027557190612001.32
250041044390310501.16
3123610472313801.65
42052657505457701.41
3783867601061
670730950995
1.771.891.250.94
1234
11.5461.6061.2851.129
21.4661.5261.2051.049
31.7111.7711.4501.294
41.5911.6511.3301.174
1234
10.0096.34353.38644.60109412001.10
273.310.00494.05464.66103210501.02
3210.48108.010.0060.813793801.00
4326.20437.4199.750.008637700.89
6106429471170
670730950995
1.101.141.000.85
1234
11.0991.1191.0510.975
21.0591.0791.0110.935
31.0491.0691.0010.925
40.9941.0140.9460.870
1234
10.00107.78371.57628.61110812001.08
277.650.00499.73434.55101210501.04
3220.83115.430.0056.263933800.97
4324.31443.4394.410.008627700.89
6236679661119
670730950995
1.081.100.980.89
1234
11.0781.0881.0320.984
21.0581.0681.0120.964
31.0231.0330.9770.929
40.9830.9930.9370.889
1234
10.00117.21383.41618.82111912001.07
282.150.00505.66419.09100710501.04
3225.89119.190.0052.293973800.96
4318.76440.1188.450.008477700.91
6276779781090
670730950995
1.071.080.970.91
1234
11.0691.0751.0210.991
21.0541.0601.0060.976
31.0141.0200.9660.936
40.9890.9950.9410.911
1234
10.00125.95391.43613.46113112001.06
286.620.00508.65409.17100410501.05
3229.16121.520.0048.964003800.95
4315.40437.7183.230.008367700.92
6316859831072
670730950995
1.061.070.970.93
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
DETROIT FACTORS HW
Observed Trips T(ij)0
1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0
10251020551152.09
225060301151501.30
31060015851351.59
4203015065951.46
sum =3204951.55= F(.)1
Iteration 1: F(ij)1 = [F(i)1 * F(j)1] / F(.)1
1234
12.8181.7532.1441.969
21.7531.0901.3341.225
32.1441.3341.6311.498
41.9691.2251.4981.375
T(ij)1 = T(ij)0 * F(ij)1
1234T(i)1T(i)^F(i)2 = T(i)^ / T(i)1
104421391051151.10
244080371611500.93
321800221241351.09
4393722099950.96
sum =4884951.01= F(.)2
Iteration 2: F(ij)2 = [F(i)2 * F(j)2] / F(.)2
1234
11.1981.0131.1871.046
21.0130.8561.0040.884
31.1871.0041.1761.036
41.0460.8841.0360.912
T(ij)2 = T(ij)1 * F(ij)2
1234T(i)2T(i)^F(i)3 = T(i)^ / T(i)2
104425411111151.04
244080321571500.95
325800231291351.05
4413223097950.98
sum =4944951.00= F(.)3
Iteration 3: F(ij)3 = [F(i)3 * F(j)3] / F(.)3
1234
11.0820.9881.0921.019
20.9880.9030.9980.931
31.0920.9981.1031.029
41.0190.9311.0290.960
T(ij)3 = T(ij)2 * F(ij)3
1234T(i)3T(i)^F(i)4 = T(i)^ / T(i)3
104428421141151.01
244080301541500.97
328800241321351.02
4423024096950.99
sum =4964951.00= F(.)4
Iteration 4: F(ij)4 = [F(i)4 * F(j)4] / F(.)4
1234
11.0200.9801.0301.000
20.9800.9410.9890.960
31.0300.9891.0401.010
41.0000.9601.0100.980
T(ij)4 = T(ij)3 * F(ij)4
1234T(i)4T(i)^F(i)5 = T(i)^ / T(i)4
104329421141151.01
243079291511500.99
329790241321351.02
4422924095951.00
sum =492495
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
FRATAR METHOD HW
Observed Trips T(ij)0
1234T(i)0T(i)^F(i)1Sum(z) T(iz)0 F(z)1
10251020551152.0978
225060301151501.30191
31060015851351.59121
4203015065951.46105
Iteration 1: t(ij)1 = T(ij)0 T(i)^ F(j)1 / Sum(z) {T(iz)0 F(z)1]
1234
10482443
24107534
32387024
43835220
T(ij)1 = [t(ij)1 + t(ji)1] / 2
1234T(i)1T(i)^F(i)2Sum(z) T(iz)1 F(z)2
104523411091151.06106
245081351601500.94167
323810231271351.06123
4413523099950.96100
Iteration 2: t(ij)2 = T(ij)1 T(i)^ F(j)2 / Sum(z) {T(iz)1 F(z)2]
1234
10462742
24307730
32783024
44131230
T(ij)2 = [t(ij)2 + t(ji)2] / 2
1234T(i)2T(i)^F(i)3Sum(z) T(iz)2 F(z)3
104427421131151.02112
244080311551500.97158
327800241311351.03129
4423124096950.9997
Iteration 3: t(ij)3 = T(ij)2 T(i)^ F(j)3 / Sum(z) {T(iz)2 F(z)3]
1234
10442942
24307929
32981025
44229240
T(ij)3 = [t(ij)3 + t(ji)3] / 2
1234T(i)3T(i)^F(i)4
104329421141151.01
243080291521500.98
329800241331351.01
4422924095951.00
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
SC Growth Model HW
Singly-constrained by Originating
1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0
106027557190612001.32
250041044390310501.16
3123610472313801.65
42052657505457701.41
3783867601061
1234
10793637541196
25804765141047
3203101078381
42893741060768
550553.5944.351345.15
Singly-constrained by Destined
1234T(i)0T(i)^
10602755719061200
25004104439031050
312361047231380
4205265750545770
T(i)03783867601061
T(i)^670730950995
F(i)1 = T(i)^ / T(i)01.771.891.250.94
1234
10113344537994
28905134161017
3218115044377
4363501940957
669730950997
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
Average Factors HW
Observed Trips tij(0)
1234ti(0)TiFi(1) = Ti / ti(0)
106027557190612001.32
250041044390310501.16
3123610472313801.65
42052657505457701.41
Tj(0)3783867601061
Tj^670730950995
Fj(1) = Tj^ / Tj(0)1.771.891.250.94
Iteration 1: Fij(1) = [Fi(1) + Fj(1)] / 2
1234
11.5461.6061.2851.129
21.4661.5261.2051.049
31.7111.7711.4501.294
41.5911.6511.3301.174
Tij(1) = Tij(0) * Fij(1)
1234Ti(1)Ti^Fi(2) = Ti^ / Ti(1)
10.0096.34353.38644.60109412001.10
273.310.00494.05464.66103210501.02
3210.48108.010.0060.813793801.00
4326.20437.4199.750.008637700.89
Tj(1)6106429471170
Tj^670730950995
Fj(2) = Tj^ / Tj(1)1.101.141.000.85
Iteration 2: Fij(2) = [Fi(2) + Fj(2)] / 2
1234
11.0991.1191.0510.975
21.0591.0791.0110.935
31.0491.0691.0010.925
40.9941.0140.9460.870
Tij(2) = Tij(1) * Fij(2)
1234Ti(2)Ti^Fi(3) = Ti^ / Ti(2)
10.00107.78371.57628.61110812001.08
277.650.00499.73434.55101210501.04
3220.83115.430.0056.263933800.97
4324.31443.4394.410.008627700.89
Tj(2)6236679661119
Tj^670730950995
Fj(2) = Tj^ / Tj(1)1.081.100.980.89
Iteration 3: Fij(3) = [Fi(3) + Fj(3)] / 2
1234
11.0781.0881.0320.984
21.0581.0681.0120.964
31.0231.0330.9770.929
40.9830.9930.9370.889
Tij(3) = Tij(2) * Fij(3)
1234Ti(3)Ti^Fi(4) = Ti^ / Ti(3)
10.00117.21383.41618.82111912001.07
282.150.00505.66419.09100710501.04
3225.89119.190.0052.293973800.96
4318.76440.1188.450.008477700.91
Tj(3)6276779781090
Tj^670730950995
Fj(4) = Tj^ / Tj(3)1.071.080.970.91
Iteration 4: Fij(4) = [Fi(4) + Fj(4)] / 2
1234
11.0691.0751.0210.991
21.0541.0601.0060.976
31.0141.0200.9660.936
40.9890.9950.9410.911
Tij(4) = Tij(3) * Fij(4)
1234Ti(4)Ti^Fi(5) = Ti^ / Ti(4)
10.00125.95391.43613.46113112001.06
286.620.00508.65409.17100410501.05
3229.16121.520.0048.964003800.95
4315.40437.7183.230.008367700.92
Tj(4)6316859831072
Tj^670730950995
Fj(5) = Tj^ / Tj(4)1.061.070.970.93
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
DETROIT FACTORS HW
Observed Trips T(ij)0
1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0
10251020551152.09
225060301151501.30
31060015851351.59
4203015065951.46
sum =3204951.55= F(.)1
Iteration 1: F(ij)1 = [F(i)1 * F(j)1] / F(.)1
1234
12.8181.7532.1441.969
21.7531.0901.3341.225
32.1441.3341.6311.498
41.9691.2251.4981.375
T(ij)1 = T(ij)0 * F(ij)1
1234T(i)1T(i)^F(i)2 = T(i)^ / T(i)1
104421391051151.10
244080371611500.93
321800221241351.09
4393722099950.96
sum =4884951.01= F(.)2
Iteration 2: F(ij)2 = [F(i)2 * F(j)2] / F(.)2
1234
11.1981.0131.1871.046
21.0130.8561.0040.884
31.1871.0041.1761.036
41.0460.8841.0360.912
T(ij)2 = T(ij)1 * F(ij)2
1234T(i)2T(i)^F(i)3 = T(i)^ / T(i)2
104425411111151.04
244080321571500.95
325800231291351.05
4413223097950.98
sum =4944951.00= F(.)3
Iteration 3: F(ij)3 = [F(i)3 * F(j)3] / F(.)3
1234
11.0820.9881.0921.019
20.9880.9030.9980.931
31.0920.9981.1031.029
41.0190.9311.0290.960
T(ij)3 = T(ij)2 * F(ij)3
1234T(i)3T(i)^F(i)4 = T(i)^ / T(i)3
104428421141151.01
244080301541500.97
328800241321351.02
4423024096950.99
sum =4964951.00= F(.)4
Iteration 4: F(ij)4 = [F(i)4 * F(j)4] / F(.)4
1234
11.0200.9801.0301.000
20.9800.9410.9890.960
31.0300.9891.0401.010
41.0000.9601.0100.980
T(ij)4 = T(ij)3 * F(ij)4
1234T(i)4T(i)^F(i)5 = T(i)^ / T(i)4
104329421141151.01
243079291511500.99
329790241321351.02
4422924095951.00
sum =492495
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
FRATAR METHOD HW
Observed Trips T(ij)0
1234T(i)0T(i)^F(i)1Sum(z) T(iz)0 F(z)1
10251020551152.0978
225060301151501.30191
31060015851351.59121
4203015065951.46105
Iteration 1: t(ij)1 = T(ij)0 T(i)^ F(j)1 / Sum(z) {T(iz)0 F(z)1]
1234
10482443
24107534
32387024
43835220
T(ij)1 = [t(ij)1 + t(ji)1] / 2
1234T(i)1T(i)^F(i)2Sum(z) T(iz)1 F(z)2
104523411091151.06106
245081351601500.94167
323810231271351.06123
4413523099950.96100
Iteration 2: t(ij)2 = T(ij)1 T(i)^ F(j)2 / Sum(z) {T(iz)1 F(z)2]
1234
10462742
24307730
32783024
44131230
T(ij)2 = [t(ij)2 + t(ji)2] / 2
1234T(i)2T(i)^F(i)3Sum(z) T(iz)2 F(z)3
104427421131151.02112
244080311551500.97158
327800241311351.03129
4423124096950.9997
Iteration 3: t(ij)3 = T(ij)2 T(i)^ F(j)3 / Sum(z) {T(iz)2 F(z)3]
1234
10442942
24307929
32981025
44229240
T(ij)3 = [t(ij)3 + t(ji)3] / 2
1234T(i)3T(i)^F(i)4
104329421141151.01
243080291521500.98
329800241331351.01
4422924095951.00
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
SC Growth Model HW
Singly-constrained by Originating
1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0
106027557190612001.32
250041044390310501.16
3123610472313801.65
42052657505457701.41
3783867601061
1234
10793637541196
25804765141047
3203101078381
42893741060768
550553.5944.351345.15
Singly-constrained by Destined
1234T(i)0T(i)^
10602755719061200
25004104439031050
312361047231380
4205265750545770
T(i)03783867601061
T(i)^670730950995
F(i)1 = T(i)^ / T(i)01.771.891.250.94
1234
10113344537994
28905134161017
3218115044377
4363501940957
669730950997
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
Average Factors HW
Observed Trips Tij(0)
1234Ti(0)Ti^Fi(1) = Ti^ / Ti(0)
106027557190612001.32
250041044390310501.16
3123610472313801.65
42052657505457701.41
tj(0)3783867601061
Tj^670730950995
Fj(1) = Tj^ / Tj(0)1.771.891.250.94
Iteration 1: Fij(1) = [Fi(1) + Fj(1)] / 2
1234
11.5461.6061.2851.129
21.4661.5261.2051.049
31.7111.7711.4501.294
41.5911.6511.3301.174
Tij(1) = Tij(0) * Fij(1)
1234Ti(1)Ti^Fi(2) = Ti^ / Ti(1)
10.0096.34353.38644.60109412001.10
273.310.00494.05464.66103210501.02
3210.48108.010.0060.813793801.00
4326.20437.4199.750.008637700.89
Tj(1)6106429471170
Tj^670730950995
Fj(2) = Tj^ / Tj(1)1.101.141.000.85
Iteration 2: Fij(2) = [Fi(2) + Fj(2)] / 2
1234
11.0991.1191.0510.975
21.0591.0791.0110.935
31.0491.0691.0010.925
40.9941.0140.9460.870
Tij(2) = Tij(1) * Fij(2)
1234Ti(2)Ti^Fi(3) = Ti^ / Ti(2)
10.00107.78371.57628.61110812001.08
277.650.00499.73434.55101210501.04
3220.83115.430.0056.263933800.97
4324.31443.4394.410.008627700.89
Tj(2)6236679661119
Tj^670730950995
Fj(2) = Tj^ / Tj(1)1.081.100.980.89
Iteration 3: Fij(3) = [Fi(3) + Fj(3)] / 2
1234
11.0781.0881.0320.984
21.0581.0681.0120.964
31.0231.0330.9770.929
40.9830.9930.9370.889
Tij(3) = Tij(2) * Fij(3)
1234Ti(3)Ti^Fi(4) = Ti^ / Ti(3)
10.00117.21383.41618.82111912001.07
282.150.00505.66419.09100710501.04
3225.89119.190.0052.293973800.96
4318.76440.1188.450.008477700.91
Tj(3)6276779781090
Tj^670730950995
Fj(4) = Tj^ / Tj(3)1.071.080.970.91
Iteration 4: Fij(4) = [Fi(4) + Fj(4)] / 2
1234
11.0691.0751.0210.991
21.0541.0601.0060.976
31.0141.0200.9660.936
40.9890.9950.9410.911
Tij(4) = Tij(3) * Fij(4)
1234Ti(4)Ti^Fi(5) = Ti^ / Ti(4)
10.00125.95391.43613.46113112001.06
286.620.00508.65409.17100410501.05
3229.16121.520.0048.964003800.95
4315.40437.7183.230.008367700.92
Tj(4)6316859831072
Tj^670730950995
Fj(5) = Tj^ / Tj(4)1.061.070.970.93
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
DETROIT FACTORS HW
Observed Trips T(ij)0
1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0
10251020551152.09
225060301151501.30
31060015851351.59
4203015065951.46
sum =3204951.55= F(.)1
Iteration 1: F(ij)1 = [F(i)1 * F(j)1] / F(.)1
1234
12.8181.7532.1441.969
21.7531.0901.3341.225
32.1441.3341.6311.498
41.9691.2251.4981.375
T(ij)1 = T(ij)0 * F(ij)1
1234T(i)1T(i)^F(i)2 = T(i)^ / T(i)1
104421391051151.10
244080371611500.93
321800221241351.09
4393722099950.96
sum =4884951.01= F(.)2
Iteration 2: F(ij)2 = [F(i)2 * F(j)2] / F(.)2
1234
11.1981.0131.1871.046
21.0130.8561.0040.884
31.1871.0041.1761.036
41.0460.8841.0360.912
T(ij)2 = T(ij)1 * F(ij)2
1234T(i)2T(i)^F(i)3 = T(i)^ / T(i)2
104425411111151.04
244080321571500.95
325800231291351.05
4413223097950.98
sum =4944951.00= F(.)3
Iteration 3: F(ij)3 = [F(i)3 * F(j)3] / F(.)3
1234
11.0820.9881.0921.019
20.9880.9030.9980.931
31.0920.9981.1031.029
41.0190.9311.0290.960
T(ij)3 = T(ij)2 * F(ij)3
1234T(i)3T(i)^F(i)4 = T(i)^ / T(i)3
104428421141151.01
244080301541500.97
328800241321351.02
4423024096950.99
sum =4964951.00= F(.)4
Iteration 4: F(ij)4 = [F(i)4 * F(j)4] / F(.)4
1234
11.0200.9801.0301.000
20.9800.9410.9890.960
31.0300.9891.0401.010
41.0000.9601.0100.980
T(ij)4 = T(ij)3 * F(ij)4
1234T(i)4T(i)^F(i)5 = T(i)^ / T(i)4
104329421141151.01
243079291511500.99
329790241321351.02
4422924095951.00
sum =492495
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
FRATAR METHOD HW
Observed Trips T(ij)0
1234T(i)0T(i)^F(i)1Sum(z) T(iz)0 F(z)1
10251020551152.0978
225060301151501.30191
31060015851351.59121
4203015065951.46105
Iteration 1: t(ij)1 = T(ij)0 T(i)^ F(j)1 / Sum(z) {T(iz)0 F(z)1]
1234
10482443
24107534
32387024
43835220
T(ij)1 = [t(ij)1 + t(ji)1] / 2
1234T(i)1T(i)^F(i)2Sum(z) T(iz)1 F(z)2
104523411091151.06106
245081351601500.94167
323810231271351.06123
4413523099950.96100
Iteration 2: t(ij)2 = T(ij)1 T(i)^ F(j)2 / Sum(z) {T(iz)1 F(z)2]
1234
10462742
24307730
32783024
44131230
T(ij)2 = [t(ij)2 + t(ji)2] / 2
1234T(i)2T(i)^F(i)3Sum(z) T(iz)2 F(z)3
104427421131151.02112
244080311551500.97158
327800241311351.03129
4423124096950.9997
Iteration 3: t(ij)3 = T(ij)2 T(i)^ F(j)3 / Sum(z) {T(iz)2 F(z)3]
1234
10442942
24307929
32981025
44229240
T(ij)3 = [t(ij)3 + t(ji)3] / 2
1234T(i)3T(i)^F(i)4
104329421141151.01
243080291521500.98
329800241331351.01
4422924095951.00
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
SC Growth Model HW
Singly-constrained by Originating
1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0
106027557190612001.32
250041044390310501.16
3123610472313801.65
42052657505457701.41
3783867601061
1234
10793637541196
25804765141047
3203101078381
42893741060768
550553.5944.351345.15
Singly-constrained by Destined
1234T(i)0T(i)^
10602755719061200
25004104439031050
312361047231380
4205265750545770
T(i)03783867601061
T(i)^670730950995
F(i)1 = T(i)^ / T(i)01.771.891.250.94
1234
10113344537994
28905134161017
3218115044377
4363501940957
669730950997
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
Average Factors HW
Observed Trips Tij(0)
1234ti(0)TiFi(1) = Ti / ti(0)
106027557190612001.32
250041044390310501.16
3123610472313801.65
42052657505457701.41
tj(0)3783867601061
Tj670730950995
Fj(1) = Tj / tj(0)1.771.891.250.94
Iteration 1: Fij(1) = [Fi(1) + Fj(1)] / 2
1234
11.5461.6061.2851.129
21.4661.5261.2051.049
31.7111.7711.4501.294
41.5911.6511.3301.174
Tij(1) = Tij(0) * Fij(1)
1234Ti(1)Ti^Fi(2) = Ti^ / Ti(1)
10.0096.34353.38644.60109412001.10
273.310.00494.05464.66103210501.02
3210.48108.010.0060.813793801.00
4326.20437.4199.750.008637700.89
Tj(1)6106429471170
Tj^670730950995
Fj(2) = Tj^ / Tj(1)1.101.141.000.85
Iteration 2: Fij(2) = [Fi(2) + Fj(2)] / 2
1234
11.0991.1191.0510.975
21.0591.0791.0110.935
31.0491.0691.0010.925
40.9941.0140.9460.870
Tij(2) = Tij(1) * Fij(2)
1234Ti(2)Ti^Fi(3) = Ti^ / Ti(2)
10.00107.78371.57628.61110812001.08
277.650.00499.73434.55101210501.04
3220.83115.430.0056.263933800.97
4324.31443.4394.410.008627700.89
Tj(2)6236679661119
Tj^670730950995
Fj(2) = Tj^ / Tj(1)1.081.100.980.89
Iteration 3: Fij(3) = [Fi(3) + Fj(3)] / 2
1234
11.0781.0881.0320.984
21.0581.0681.0120.964
31.0231.0330.9770.929
40.9830.9930.9370.889
Tij(3) = Tij(2) * Fij(3)
1234Ti(3)Ti^Fi(4) = Ti^ / Ti(3)
10.00117.21383.41618.82111912001.07
282.150.00505.66419.09100710501.04
3225.89119.190.0052.293973800.96
4318.76440.1188.450.008477700.91
Tj(3)6276779781090
Tj^670730950995
Fj(4) = Tj^ / Tj(3)1.071.080.970.91
Iteration 4: Fij(4) = [Fi(4) + Fj(4)] / 2
1234
11.0691.0751.0210.991
21.0541.0601.0060.976
31.0141.0200.9660.936
40.9890.9950.9410.911
Tij(4) = Tij(3) * Fij(4)
1234Ti(4)Ti^Fi(5) = Ti^ / Ti(4)
10.00125.95391.43613.46113112001.06
286.620.00508.65409.17100410501.05
3229.16121.520.0048.964003800.95
4315.40437.7183.230.008367700.92
Tj(4)6316859831072
Tj^670730950995
Fj(5) = Tj^ / Tj(4)1.061.070.970.93
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
DETROIT FACTORS HW
Observed Trips T(ij)0
1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0
10251020551152.09
225060301151501.30
31060015851351.59
4203015065951.46
sum =3204951.55= F(.)1
Iteration 1: F(ij)1 = [F(i)1 * F(j)1] / F(.)1
1234
12.8181.7532.1441.969
21.7531.0901.3341.225
32.1441.3341.6311.498
41.9691.2251.4981.375
T(ij)1 = T(ij)0 * F(ij)1
1234T(i)1T(i)^F(i)2 = T(i)^ / T(i)1
104421391051151.10
244080371611500.93
321800221241351.09
4393722099950.96
sum =4884951.01= F(.)2
Iteration 2: F(ij)2 = [F(i)2 * F(j)2] / F(.)2
1234
11.1981.0131.1871.046
21.0130.8561.0040.884
31.1871.0041.1761.036
41.0460.8841.0360.912
T(ij)2 = T(ij)1 * F(ij)2
1234T(i)2T(i)^F(i)3 = T(i)^ / T(i)2
104425411111151.04
244080321571500.95
325800231291351.05
4413223097950.98
sum =4944951.00= F(.)3
Iteration 3: F(ij)3 = [F(i)3 * F(j)3] / F(.)3
1234
11.0820.9881.0921.019
20.9880.9030.9980.931
31.0920.9981.1031.029
41.0190.9311.0290.960
T(ij)3 = T(ij)2 * F(ij)3
1234T(i)3T(i)^F(i)4 = T(i)^ / T(i)3
104428421141151.01
244080301541500.97
328800241321351.02
4423024096950.99
sum =4964951.00= F(.)4
Iteration 4: F(ij)4 = [F(i)4 * F(j)4] / F(.)4
1234
11.0200.9801.0301.000
20.9800.9410.9890.960
31.0300.9891.0401.010
41.0000.9601.0100.980
T(ij)4 = T(ij)3 * F(ij)4
1234T(i)4T(i)^F(i)5 = T(i)^ / T(i)4
104329421141151.01
243079291511500.99
329790241321351.02
4422924095951.00
sum =492495
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
FRATAR METHOD HW
Observed Trips T(ij)0
1234T(i)0T(i)^F(i)1Sum(z) T(iz)0 F(z)1
10251020551152.0978
225060301151501.30191
31060015851351.59121
4203015065951.46105
Iteration 1: t(ij)1 = T(ij)0 T(i)^ F(j)1 / Sum(z) {T(iz)0 F(z)1]
1234
10482443
24107534
32387024
43835220
T(ij)1 = [t(ij)1 + t(ji)1] / 2
1234T(i)1T(i)^F(i)2Sum(z) T(iz)1 F(z)2
104523411091151.06106
245081351601500.94167
323810231271351.06123
4413523099950.96100
Iteration 2: t(ij)2 = T(ij)1 T(i)^ F(j)2 / Sum(z) {T(iz)1 F(z)2]
1234
10462742
24307730
32783024
44131230
T(ij)2 = [t(ij)2 + t(ji)2] / 2
1234T(i)2T(i)^F(i)3Sum(z) T(iz)2 F(z)3
104427421131151.02112
244080311551500.97158
327800241311351.03129
4423124096950.9997
Iteration 3: t(ij)3 = T(ij)2 T(i)^ F(j)3 / Sum(z) {T(iz)2 F(z)3]
1234
10442942
24307929
32981025
44229240
T(ij)3 = [t(ij)3 + t(ji)3] / 2
1234T(i)3T(i)^F(i)4
104329421141151.01
243080291521500.98
329800241331351.01
4422924095951.00
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
SC Growth Model HW
Singly-constrained by Originating
1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0
106027557190612001.32
250041044390310501.16
3123610472313801.65
42052657505457701.41
3783867601061
1234
10793637541196
25804765141047
3203101078381
42893741060768
550553.5944.351345.15
Singly-constrained by Destined
1234T(i)0T(i)^
10602755719061200
25004104439031050
312361047231380
4205265750545770
T(i)03783867601061
T(i)^670730950995
F(i)1 = T(i)^ / T(i)01.771.891.250.94
1234
10113344537994
28905134161017
3218115044377
4363501940957
669730950997
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
Average Factors HW
Observed Trips tij(0)
1234Ti(0)Ti^Fi(1) = Ti^ / Ti(0)
106027557190612001.32
250041044390310501.16
3123610472313801.65
42052657505457701.41
tj(0)3783867601061
Tj670730950995
Fj(1) = Tj / tj(0)1.771.891.250.94
Iteration 1: Fij(1) = [Fi(1) + Fj(1)] / 2
1234
11.5461.6061.2851.129
21.4661.5261.2051.049
31.7111.7711.4501.294
41.5911.6511.3301.174
Tij(1) = Tij(0) * Fij(1)
1234Ti(1)Ti^Fi(2) = Ti^ / Ti(1)
10.0096.34353.38644.60109412001.10
273.310.00494.05464.66103210501.02
3210.48108.010.0060.813793801.00
4326.20437.4199.750.008637700.89
Tj(1)6106429471170
Tj^670730950995
Fj(2) = Tj^ / Tj(1)1.101.141.000.85
Iteration 2: Fij(2) = [Fi(2) + Fj(2)] / 2
1234
11.0991.1191.0510.975
21.0591.0791.0110.935
31.0491.0691.0010.925
40.9941.0140.9460.870
Tij(2) = Tij(1) * Fij(2)
1234Ti(2)Ti^Fi(3) = Ti^ / Ti(2)
10.00107.78371.57628.61110812001.08
277.650.00499.73434.55101210501.04
3220.83115.430.0056.263933800.97
4324.31443.4394.410.008627700.89
Tj(2)6236679661119
Tj^670730950995
Fj(2) = Tj^ / Tj(1)1.081.100.980.89
Iteration 3: Fij(3) = [Fi(3) + Fj(3)] / 2
1234
11.0781.0881.0320.984
21.0581.0681.0120.964
31.0231.0330.9770.929
40.9830.9930.9370.889
Tij(3) = Tij(2) * Fij(3)
1234Ti(3)Ti^Fi(4) = Ti^ / Ti(3)
10.00117.21383.41618.82111912001.07
282.150.00505.66419.09100710501.04
3225.89119.190.0052.293973800.96
4318.76440.1188.450.008477700.91
Tj(3)6276779781090
Tj^670730950995
Fj(4) = Tj^ / Tj(3)1.071.080.970.91
Iteration 4: Fij(4) = [Fi(4) + Fj(4)] / 2
1234
11.0691.0751.0210.991
21.0541.0601.0060.976
31.0141.0200.9660.936
40.9890.9950.9410.911
Tij(4) = Tij(3) * Fij(4)
1234Ti(4)Ti^Fi(5) = Ti^ / Ti(4)
10.00125.95391.43613.46113112001.06
286.620.00508.65409.17100410501.05
3229.16121.520.0048.964003800.95
4315.40437.7183.230.008367700.92
Tj(4)6316859831072
Tj^670730950995
Fj(5) = Tj^ / Tj(4)1.061.070.970.93
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
DETROIT FACTORS HW
Observed Trips T(ij)0
1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0
10251020551152.09
225060301151501.30
31060015851351.59
4203015065951.46
sum =3204951.55= F(.)1
Iteration 1: F(ij)1 = [F(i)1 * F(j)1] / F(.)1
1234
12.8181.7532.1441.969
21.7531.0901.3341.225
32.1441.3341.6311.498
41.9691.2251.4981.375
T(ij)1 = T(ij)0 * F(ij)1
1234T(i)1T(i)^F(i)2 = T(i)^ / T(i)1
104421391051151.10
244080371611500.93
321800221241351.09
4393722099950.96
sum =4884951.01= F(.)2
Iteration 2: F(ij)2 = [F(i)2 * F(j)2] / F(.)2
1234
11.1981.0131.1871.046
21.0130.8561.0040.884
31.1871.0041.1761.036
41.0460.8841.0360.912
T(ij)2 = T(ij)1 * F(ij)2
1234T(i)2T(i)^F(i)3 = T(i)^ / T(i)2
104425411111151.04
244080321571500.95
325800231291351.05
4413223097950.98
sum =4944951.00= F(.)3
Iteration 3: F(ij)3 = [F(i)3 * F(j)3] / F(.)3
1234
11.0820.9881.0921.019
20.9880.9030.9980.931
31.0920.9981.1031.029
41.0190.9311.0290.960
T(ij)3 = T(ij)2 * F(ij)3
1234T(i)3T(i)^F(i)4 = T(i)^ / T(i)3
104428421141151.01
244080301541500.97
328800241321351.02
4423024096950.99
sum =4964951.00= F(.)4
Iteration 4: F(ij)4 = [F(i)4 * F(j)4] / F(.)4
1234
11.0200.9801.0301.000
20.9800.9410.9890.960
31.0300.9891.0401.010
41.0000.9601.0100.980
T(ij)4 = T(ij)3 * F(ij)4
1234T(i)4T(i)^F(i)5 = T(i)^ / T(i)4
104329421141151.01
243079291511500.99
329790241321351.02
4422924095951.00
sum =492495
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
FRATAR METHOD HW
Observed Trips T(ij)0
1234T(i)0T(i)^F(i)1Sum(z) T(iz)0 F(z)1
10251020551152.0978
225060301151501.30191
31060015851351.59121
4203015065951.46105
Iteration 1: t(ij)1 = T(ij)0 T(i)^ F(j)1 / Sum(z) {T(iz)0 F(z)1]
1234
10482443
24107534
32387024
43835220
T(ij)1 = [t(ij)1 + t(ji)1] / 2
1234T(i)1T(i)^F(i)2Sum(z) T(iz)1 F(z)2
104523411091151.06106
245081351601500.94167
323810231271351.06123
4413523099950.96100
Iteration 2: t(ij)2 = T(ij)1 T(i)^ F(j)2 / Sum(z) {T(iz)1 F(z)2]
1234
10462742
24307730
32783024
44131230
T(ij)2 = [t(ij)2 + t(ji)2] / 2
1234T(i)2T(i)^F(i)3Sum(z) T(iz)2 F(z)3
104427421131151.02112
244080311551500.97158
327800241311351.03129
4423124096950.9997
Iteration 3: t(ij)3 = T(ij)2 T(i)^ F(j)3 / Sum(z) {T(iz)2 F(z)3]
1234
10442942
24307929
32981025
44229240
T(ij)3 = [t(ij)3 + t(ji)3] / 2
1234T(i)3T(i)^F(i)4
104329421141151.01
243080291521500.98
329800241331351.01
4422924095951.00
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
SC Growth Model HW
Singly-constrained by Originating
1234T(i)0T(i)^F(i)1 = T(i)^ / T(i)0
106027557190612001.32
250041044390310501.16
3123610472313801.65
42052657505457701.41
3783867601061
1234
10793637541196
25804765141047
3203101078381
42893741060768
550553.5944.351345.15
Singly-constrained by Destined
1234T(i)0T(i)^
10602755719061200
25004104439031050
312361047231380
4205265750545770
T(i)03783867601061
T(i)^670730950995
F(i)1 = T(i)^ / T(i)01.771.891.250.94
1234
10113344537994
28905134161017
3218115044377
4363501940957
669730950997
&CCE 370 - Transportation Planning - Trip DistributionGrowth Factor Models - &A
Average Factors HW
Observed Trips Tij(0)
1234Ti(0)Ti^Fi(1) = Ti / ti(0)
106027557190612001.32
250041044390310501.16
3123610472313801.65
42052657505457701.41
tj(0)3783867601061
Tj670730950995
Fj(1) = Tj / tj(0)1.771.891.250.94
Iteration 1: Fij(1) = [Fi(1) + Fj(1)] / 2
1234
11.5461.6061.2851.129
21.4661.5261.2051.049
31.7111.7711.4501.294
41.5911.6511.3301.174
Tij(1) = Tij(0) * Fij(1)
1234Ti(1)Ti^Fi(2) = Ti^ / Ti(1)
10.0096.34353.38644.60109412001.10
273.310.004