Topic 5 - Platoon Dispersion
Download
Report
Transcript Topic 5 - Platoon Dispersion
Topic 5
Platoon and Dispersion
CEE 764 – Fall 2010
TRANSYT-7F MODEL
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?
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
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
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