matts: university of delft, 2018
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MATTS: University of Delft, 2018
Dynamical queueing, dynamical route choice,
responsive traffic control and control systems
which maximise network throughput
Michael J. Smith, Takamasa Iryo, Richard
Mounce, Marco Rinaldi, and Francesco Viti
Universities:
York, Kobe, Aberdeen, Luxembourg
Route 1
ORIGINDESTINATION
O DB
Route 2
BOTTLENECK
Dynamical queueing
Route 1
ORIGINDESTINATION
O DB
Route 2
BOTTLENECKQUEUE
Dynamical queueing
Route 1
ORIGINDESTINATION
O DB
Route 2
BOTTLENECKQUEUE
Dynamical queueing
Route 1
ORIGINDESTINATION
O DB
Route 2
BOTTLENECKQUEUE
Dynamical queueing
Route 1
ORIGINDESTINATION
O DB
Route 2
BOTTLENECKQUEUE
Dynamical queueing
Route 1
ORIGINDESTINATION
O DB
Route 2
BOTTLENECKQUEUE
Dynamical queueing
Route 1
ORIGINDESTINATION
O DB
Route 2
BOTTLENECKQUEUE
Dynamical queueing
Route 1
ORIGINDESTINATION
O DB
Route 2
BOTTLENECKQUEUE
Dynamical queueing
Route 1
ORIGINDESTINATION
O DB
Route 2
BOTTLENECKQUEUE
(STATIONARY)
Dynamical queueing
SMALL Network
OriginDestination
Stage 1 S
Signal: (g1, g2)
Stage 2
bottleneck delay b2
bottleneck delay b1
X2 = route 2 flow
X1
Sat flow s2=2
Sat flow s1=1
SMALL Network is not unrealistic
Destination
SMALL Network is not unrealistic
Destination
SMALL Network is not unrealistic
Destination
1
SMALL Network is not unrealistic
Destination
1
SMALL Network is not unrealistic
Destination
1
2
SMALL Network is not unrealistic
Destination
1
2
SMALL Network is not unrealistic
Destination
1
23
Summary
The talk considers:
- A spatial queueing model (representing the space taken up by queues)
- Traffic signal control and route choice.
- Throughput maximising control when demand exceeds capacity
- P0 control and pricing results for the City of York.
Summary
The talk considers:
- A spatial queueing model (representing the space taken up by queues)
DONE
- Traffic signal control and route choice.
- Throughput maximising control when demand exceeds capacity
- P0 control and pricing results for the City of York.
AIM
TO REDUCE CONGESTION /
POLLUTION IN CITIES
AIM
TO REDUCE CONGESTION /
POLLUTION IN CITIES
IN PART AUTOMATICALLY
Modelling Signal Control and Route
Choice: Allsop, Dickson, Gartner, Akcelik, Maher, Van Vliet,
Van Vuren, Smith, Van Zuylen, Meneguzzer, Gentile,
Noekel, Taale, Cantarella, Mounce, Watling, Ke Han,
Himpe, Viti, Schlaich, Haupt, Tampere, Huang, Rinaldi,
●
●
●
Previous Work
Traffic Control and Route Choice
Traffic Control Route Choice
NETWORK WITH ROUTE AND
GREEN-TIME CHOICES
ORIGIN DESTINATION
Stage 1 S
Signal: (g1, g2)Stage 2
b2 = bottleneck delay
bottleneck delay b1
NETWORK WITH ROUTE AND
GREEN-TIME CHOICES
ORIGIN DESTINATION
Stage 1 SRoute 1
Signal: (g1, g2)Stage 2
Route 2, cost C2
cost C1
b2 = bottleneck delay
bottleneck delay b1
Control and Route-flow VariablesControls:
Green-time vector g:
g1+g2 = 1.
Route-flows:
Route-flow vector X;
X1+X2 = given steady demand T.
SMALL Network
ORIGINDestination
Stage 1 S
Signal: (g1, g2)
Stage 2
bottleneck delay b2
bottleneck delay b1
X2 = route 2 flow
X1
Sat flow s2=2 (v/s)
Sat flow s1=1 (v/s)
P0: Choose greens so b is “normal” to S.
• ,
0 X1 s1
2s
X2
S
DESTINATIONSIGNAL
ORIGIN
P0
X1 + X2 = T
(X1, X2)
(b1, b2)
s2
s1
s2 = 2
X2
P0: Choose greens so b is “normal” to S.
• ,
0 X1 s
s2 = 2
X2 S(X1, X2)
(b1, b2)
s1b1 = s2b2
Demand
MAX/2 MAX
Standard
P0
OPT
STANDARD POLICIES HALVE THE
CAPACITY OF THIS NETWORK
Average
journey
time
NETWORK WITH ROUTE AND
GREEN-TIME CHOICES
ORIGIN DESTINATION
Stage 1 S
Signal: (g1, g2)Stage 2
b2 = bottleneck delay
bottleneck delay b1
Equilibrium flow and P0 green-time
EXACT P0 Control Policy:
green-time g satisfies s1b1 = s2b2
EXACT route-choice equilibrium:
route-flow X satisfies C1+b1 = C2+b2
What if these conditions do not hold?
ROUTE AND GREEN-TIME SWAPS
ORIGIN DESTINATION
Stage 1 SRoute 1
Route 2SIGNALStage 2
ROUTE AND GREEN-TIME SWAPS
ORIGIN DESTINATION
Stage 1 SRoute 1
Route 2SIGNALStage 2
Travel cost along route 1 = C1+b1
Travel cost along route 2 = C2+b2
ROUTE AND GREEN-TIME SWAPS
ORIGIN DESTINATION
Stage 1 SRoute 1
Route 2SIGNALStage 2
Travel cost along route 1 = C1+b1
Travel cost along route 2 = C2+b2
ROUTE AND GREEN-TIME SWAPS
ORIGIN DESTINATION
Stage 1 SRoute 1
Route 2SIGNALStage 2
Pressure on stage 1 = s1b1
Pressure on stage 2 = s2b2
ROUTE AND GREEN-TIME SWAPS
ORIGIN DESTINATION
Stage 1 SRoute 1
Route 2SIGNALStage 2
s1b1 - s2b2
controls green arrow
[C1+b1] – [C2+b2]
controls black arrow
*** HOPE: Stability ***V(X,g) = 4
V(X,g) = 2
V(X,g) = 1
V(X,g) = 3
EQUILIBRIUM:
V(X,g) = minimum
*** HOPE: Stability ***V(X,g) = 4
V(X,g) = 2
V(X,g) = 1
V(X,g) = 3
EQUILIBRIUM:
V(X,g) = minimum
●
*** HOPE: Stability ***V(X,g) = 4
V(X,g) = 2
V(X,g) = 1
V(X,g) = 3
EQUILIBRIUM:
V(X,g) = minimum
●
●
*** HOPE: Stability ***V(X,g) = 4
V(X,g) = 2
V(X,g) = 1
V(X,g) = 3
EQUILIBRIUM:
V(X,g) = minimum
●
●
●
*** HOPE: Stability ***V(X,g) = 4
V(X,g) = 2
V(X,g) = 1
V(X,g) = 3
EQUILIBRIUM:
V(X,g) = minimum
●
●
●
●
*** HOPE: Stability ***V(X,g) = 4
V(X,g) = 2
V(X,g) = 1
V(X,g) = 3
EQUILIBRIUM:
V(X,g) = minimum
●
●
●
●
●
HOPE: WITH P0 MANY DYNAMICAL
MODELS HAVE STABILITY!!!
EQUILIBRIUM:
V(X,g) = minimum
●
●
●
●
●
Other policies?
STABLE WITH STANDARD POLICIES ???
Other policies?
STABLE WITH STANDARD POLICIES ???
NO!
CONTROL WHICH
MAXIMISES
THROUGHPUT
Even when demand
exceeds capacity
ORIGIN
DESTINATION
SIGNAL
ss
G
1-G
ORIGIN
DESTINATION
SIGNAL
ss
MAXIMUM FLOW = s/2
G
1-G
00 s/2 D
1
1/2
G
00 s/2 D
1
1/2
G
00 s/2 D
1
1/2
G
00 s/2 D
1
1/2
G
OK
00 s/2 D
1
1/2
G
OK
NOT OK
00 s/2 D
1
1/2
G
SUMMARY
P0 modified maximises
throughput of ONE network even
when demand exceeds capacity
SUMMARY
P0 modified maximises
throughput of ONE network even
when demand exceeds capacity
Further work: Generalise!!!
QUESTIONS?
Other related work
Le, T., Kovacs, P., Walton, N., Vu, H. L.,
Andrew, L. H., Hoogendoorn, S. P. 2015.
Decentralised Signal Control for Urban Road
Networks. Transportation Research Part C,
58, 431-450. (Proportional Control Policy)
Peter Kovacs, Tung Le, Rudesindo Nunez-
Queija, Hai L. Vu, Neil Walton, Proportional
green time scheduling for traffic lights.
YORK RESULTS
These were obtained by Mustapha
Ghali using a dynamic
equilibrium program called
CONTRAM (used to be supported
by the Transport and Road
Research Laboratory in the UK)
Questions?
P0: s1b1 = s2b2
1 BA
C2=C1+Δ
C1
b2
b1
P0: s1b1 = s2b2
P0 with prices: s1p1 = s2p2
1 BA
C2=C1+Δ
C1
p2
p1
P0: s1b1 = s2b2
P0 with prices: s1p1 = s2p2
1 BA
C2
C1
p2
p1
Prices do not
block back
P0: s1b1 = s2b2
P0 with prices: s1p1 = s2p2 FEASIBLE EQM
1 BA
C2
C1
p2
p1
Prices do not
block back
P0: s1b1 = s2b2 NO FEASIBLE EQM
P0 with prices: s1p1 = s2p2 FEASIBLE EQM
1 BA
C2
C1
b2
b1
P0: s1b1 = s2b2 NO FEASIBLE EQM
P0 with prices: s1p1 = s2p2 FEASIBLE EQM
1 BA
C2
C1
b2
b1
UNBOUNDED QUEUES and DELAYS
P0: s1b1 = s2b2 NO FEASIBLE EQM
P0 with prices: s1p1 = s2p2 FEASIBLE EQM
1 BA
C2
C1
b2
b1
UNBOUNDED QUEUES and DELAYS
P0: s1b1 = s2b2
P0 with prices: s1p1 = s2p2
1 BA
C2
C1
p2
p1
Questions?
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