matts: university of delft, 2018

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

(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


Destination

1


Destination

1

2


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,

●

●

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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


GREEN-TIME CHOICES

ORIGIN DESTINATION

Stage 1 SRoute 1


Route 2, cost C2

cost C1


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


GREEN-TIME CHOICES

ORIGIN DESTINATION

Stage 1 S



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


ORIGIN DESTINATION

Stage 1 SRoute 1


Travel cost along route 1 = C1+b1

Travel cost along route 2 = C2+b2


ORIGIN DESTINATION

Stage 1 SRoute 1


Pressure on stage 1 = s1b1

Pressure on stage 2 = s2b2


ORIGIN DESTINATION

Stage 1 SRoute 1


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


V(X,g) = 2

V(X,g) = 1

V(X,g) = 3

EQUILIBRIUM:

V(X,g) = minimum

●


V(X,g) = 2

V(X,g) = 1

V(X,g) = 3

EQUILIBRIUM:

V(X,g) = minimum

●

●


V(X,g) = 2

V(X,g) = 1

V(X,g) = 3

EQUILIBRIUM:

V(X,g) = minimum

●

●

●


V(X,g) = 2

V(X,g) = 1

V(X,g) = 3

EQUILIBRIUM:

V(X,g) = minimum

●

●

●

●


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

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


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


1 BA

C2

C1

b2

b1

P0: s1b1 = s2b2 NO FEASIBLE EQM


1 BA

C2

C1

b2

b1

UNBOUNDED QUEUES and DELAYS

P0: s1b1 = s2b2


1 BA

C2

C1

p2

p1

Questions?

matts: university of delft, 2018

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