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CEE 764 – Fall 2010 CEE 764 – Fall 2010 Topic 5 Topic 5 Platoon and Dispersion Platoon and Dispersion
CEE 764 – Fall 2010CEE 764 – Fall 2010
Topic 5Topic 5Platoon and DispersionPlatoon and Dispersion
CEE 764 – Fall 2010CEE 764 – Fall 2010
TRANSYT-7F MODELTRANSYT-7F MODEL
TRANSYTTRANSYT is a computer traffic flow and signal timing is a computer traffic flow and signal timing model, originally developed in UK.model, originally developed in UK.
TRANSYT-7FTRANSYT-7F is a U.S. version of the TRANSYT model, is a U.S. version of the TRANSYT model, developed at U of Florida (Ken Courage)developed at U of Florida (Ken Courage)
TRANSYT-7F has an TRANSYT-7F has an optimizationoptimization component and a component and a simulationsimulation component. component.
The simulation component is considered as a The simulation component is considered as a macroscopicmacroscopic traffic simulation, where vehicles are traffic simulation, where vehicles are analyzed as groups. analyzed as groups.
One of the well known elements about TRANSYT-7F’s One of the well known elements about TRANSYT-7F’s traffic flow model is the traffic flow model is the Platoon DispersionPlatoon Dispersion model. model.
CEE 764 – Fall 2010CEE 764 – Fall 2010
WHY MODEL PLATOON DISPERSION?WHY MODEL PLATOON DISPERSION?
Platoons originated at traffic signals Platoons originated at traffic signals disperse disperse over time and space.over time and space.
Platoon dispersion creates non-uniform vehicle Platoon dispersion creates non-uniform vehicle arrivals at the downstream signal.arrivals at the downstream signal.
Non-uniform vehicle arrivals affect the Non-uniform vehicle arrivals affect the calculation of vehicle delayscalculation of vehicle delays at signalized at signalized intersections.intersections.
Effectiveness of signal timing and progression Effectiveness of signal timing and progression diminishes when platoons are fully dispersed diminishes when platoons are fully dispersed (e.g., due to long signal spacing).(e.g., due to long signal spacing).
CEE 764 – Fall 2010CEE 764 – Fall 2010
PLATOON DISPERSION MODELPLATOON DISPERSION MODEL
For each time interval (step), For each time interval (step), tt, the arrival flow at the downstream , the arrival flow at the downstream stopline (ignoring the presence of a queue) is found by solving the stopline (ignoring the presence of a queue) is found by solving the recursive equationrecursive equation
])1[( )1()( tTttT QFqFQ
TF
11
trafficlighttrafficratemode
trafficheavy
25.035.050.0
)(flow-free, stepstimetravelTTT
CEE 764 – Fall 2010CEE 764 – Fall 2010
PLATOON DISPERSIONPLATOON DISPERSION
Flow rate at interval t, qt
% S
atur
atio
n
0
50
100
Time, secStart Green
Flow rate at interval t + T, Q(T+t)
0
50
100
Time, sec
% S
atur
atio
n
T = 0.8 * T’
CEE 764 – Fall 2010CEE 764 – Fall 2010
CLOSED-FORM PLATOON CLOSED-FORM PLATOON DISPERSION MODELDISPERSION MODEL
Time
Flow
rate
, vp
h
0 tq tg
C
s
v
CEE 764 – Fall 2010CEE 764 – Fall 2010
CLOSED-FORM PLATOON CLOSED-FORM PLATOON DISPERSION MODEL (1~tDISPERSION MODEL (1~tqq))
])1[( )1()( tTttT QFqFQ
)0()0()1()1( )1()1( TTT QFFsQFFqQ
)0T(2
)0T()1T()2T(
Q)F1(Fs)F1(Fs
]Q)F1(Fs)[F1(FsQ)F1(FsQ
)0T(32
)2T()3T( Q)F1(Fs)F1(Fs)F1(FsQ)F1(FsQ
)0T(t)1t(2
)tT( Q)F1(Fs)F1(.......Fs)F1(Fs)F1(FsQ
For 1~tq with s flow
CEE 764 – Fall 2010CEE 764 – Fall 2010
CLOSED-FORM PLATOON CLOSED-FORM PLATOON DISPERSION MODEL (0~tDISPERSION MODEL (0~tqq))
)0T(t)1t(2
)tT( Q)F1(Fs)F1(.......Fs)F1(Fs)F1(FsQ
)0()1()()1(2
)( )1()1()1(.......)1()1()1(
Tttt
tT QFFsFFsFFsFFsFQF
(1)
(2)
(1) – (2)
F)F1(Q])F1(1[Fs
Q)F1(Fs)F1(Q)F1(FsFQt
)0T(t
)0T()1t(t
)0T(t
)tT(
)0T(tt
)tT( Q)F1(])F1(1[sQ
CEE 764 – Fall 2010CEE 764 – Fall 2010
CLOSED-FORM PLATOON CLOSED-FORM PLATOON DISPERSION MODEL (1~tDISPERSION MODEL (1~tqq))
qt
tTs ttFsQQ q
q~1],)1(1[)(max,
)0T(tt
)tT( Q)F1(])F1(1[sQ
0)0( TQ
])1(1[)(t
tT FsQ For 1~tq with s flow
Maximum flow downstream occurs at T+tq with upstream s flow
CEE 764 – Fall 2010CEE 764 – Fall 2010
BEYOND (1~tBEYOND (1~tqq))
)0T(tt
)tT( Q)F1(])F1(1[sQ
s no longer exists, but zero flow upstream
t = tq +1 ~ ∞
From the original equation:
max,)0( sT QQ
max,)( )1( stt
tT QFQ q
•This is mainly to disperse the remaining flow, Qs,max. Upstream flow is zero•The same procedure for the non-platoon flow•The final will be the sum of the two
CEE 764 – Fall 2010CEE 764 – Fall 2010
EXAMPLEEXAMPLE
Vehicles discharge from an upstream signalized intersection Vehicles discharge from an upstream signalized intersection at the following flow profile. Predict the traffic flow profile at at the following flow profile. Predict the traffic flow profile at 880 ft downstream, assuming free-flow speed of 30 mph, 880 ft downstream, assuming free-flow speed of 30 mph, αα = = 0.35; 0.35; ββ = 0.8. = 0.8. Use time step = 1 sec/step Use time step = 1 sec/step
Time
Flow
rate
, vp
h
0 16 28C=60 sec
3600
1200
CEE 764 – Fall 2010CEE 764 – Fall 2010
Platoon Dispersion (Start of Upstream Green)
0500
1000150020002500300035004000
13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85
Time Slice, sec
Flow
Rat
e, v
ph
green red
