# Topic 5 - Platoon Dispersion

```Topic 5
Platoon and Dispersion
CEE 764 – Fall 2010
TRANSYT-7F MODEL
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TRANSYT is a computer traffic flow and signal timing
model, originally developed in UK.
TRANSYT-7F is a U.S. version of the TRANSYT model,
developed at U of Florida (Ken Courage)
TRANSYT-7F has an optimization component and a
simulation component.
The simulation component is considered as a
macroscopic traffic simulation, where vehicles are
analyzed as groups.
One of the well known elements about TRANSYT-7F’s
traffic flow model is the Platoon Dispersion model.
CEE 764 – Fall 2010
WHY MODEL PLATOON DISPERSION?
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Platoons originated at traffic signals disperse
over time and space.
 Platoon dispersion creates non-uniform vehicle
arrivals at the downstream signal.
 Non-uniform vehicle arrivals affect the
calculation of vehicle delays at signalized
intersections.
 Effectiveness of signal timing and progression
diminishes when platoons are fully dispersed
(e.g., due to long signal spacing).
CEE 764 – Fall 2010
PLATOON DISPERSION MODEL
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For each time interval (step), t, the arrival flow at the downstream
stopline (ignoring the presence of a queue) is found by solving the
recursive equation
Q(T t )  F  qt  [(1  F )  Q(T t 1) ]
T    T , T   free- flow travel time (steps)
F
1
1  T
  0.50 heavytraffic
  0.35 m oderate traffic
  0.25 light traffic
CEE 764 – Fall 2010
% Saturation
PLATOON DISPERSION
Flow rate at interval t, qt
100
50
0
Time, sec
Start Green
% Saturation
T = 0.8 * T’
100
Flow rate at interval t + T, Q(T+t)
50
0
Time, sec
CEE 764 – Fall 2010
CLOSED-FORM PLATOON
DISPERSION MODEL
Flow rate, vph
s
v
0
tq
tg
C
CEE 764 – Fall 2010
Time
CLOSED-FORM PLATOON
DISPERSION MODEL (1~tq)
For 1~tq with s flow
Q(T t )  F  qt  [(1  F )  Q(T t 1) ]
Q(T 1)  Fq(1)  (1  F )Q(T 0)  Fs  (1  F )Q(T 0)
Q( T  2 )  Fs  ( 1  F )Q( T 1 )  Fs  ( 1  F )[ Fs  ( 1  F )Q( T 0 ) ]
 Fs  ( 1  F )Fs  ( 1  F ) 2 Q( T 0 )
Q( T 3 )  Fs  ( 1  F )Q( T 2 )  Fs  ( 1  F )Fs  ( 1  F )2 Fs  ( 1  F )3 Q( T 0 )
Q( T t )  Fs  ( 1  F )Fs  ( 1  F )2 Fs  ....... ( 1  F )( t 1 ) Fs  ( 1  F )t Q( T 0 )
CEE 764 – Fall 2010
CLOSED-FORM PLATOON
DISPERSION MODEL (0~tq)
(1)
Q( T t )  Fs  ( 1  F )Fs  ( 1  F )2 Fs  ....... ( 1  F )( t 1 ) Fs  ( 1  F )t Q( T 0 )
(2)
(1 F )Q(T t )  (1 F )Fs  (1 F )2 Fs  ....... (1 F )(t 1) Fs  (1 F )(t ) Fs  (1 F )(t 1) Q(T 0)
(1) – (2)
FQ( T t )  Fs  ( 1  F )t Q( T 0 )  ( 1  F )t Fs  ( 1  F )( t 1 ) Q( T 0 )
 Fs[ 1  ( 1  F )t ]  Q( T 0 ) ( 1  F )t F
Q( T t )  s[ 1  ( 1  F )t ]  ( 1  F )t Q( T 0 )
CEE 764 – Fall 2010
CLOSED-FORM PLATOON
DISPERSION MODEL (1~tq)
Q( T t )  s[ 1  ( 1  F )t ]  ( 1  F )t Q( T 0 )
Q(T 0)  0
Q(T t )  s[1  (1  F )t ]
Qs ,max  Q(T tq )  s[1  (1  F ) q ],
t
Maximum flow downstream occurs at
T+tq with upstream s flow
CEE 764 – Fall 2010
For 1~tq with s flow
t  1 ~ tq
BEYOND (1~tq)
From the original equation:
Q( T t )  s[ 1  ( 1  F )t ]  ( 1  F )t Q( T 0 )
Q(T 0)  Qs,max
Q(T t )  (1  F )
s no longer exists, but zero flow upstream
t t q
Qs ,max
t = tq +1 ~ ∞
•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 2010
EXAMPLE
Vehicles discharge from an upstream signalized intersection
at the following flow profile. Predict the traffic flow profile at
880 ft downstream, assuming free-flow speed of 30 mph, α =
0.35; β = 0.8.
Use time step = 1 sec/step
3600
Flow rate, vph
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1200
0
CEE 764 – Fall 2010
16
28
C=60 sec
Time
Flow Rate, vph
Platoon Dispersion (Start of Upstream Green)
4000
3500
3000
2500
2000
1500
1000
500
0
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
green
CEE 764 – Fall 2010
red
Time Slice, sec
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