Presentation from NORTHMOST - a new biannual series of meetings on the topic of mathematical modelling in transport.
Hosted at its.leeds.ac.uk, NORTHMOST 01 focussed on academic research, to encourage networking and collaboration between academics interested in the methodological development of mathematical modelling applied to transport.
The focus of the meetings will alternate; NORTHMOST 02 - planned for Spring 2017 - will be led by practitioners who are modelling experts. Practitioners will give presentations, with academic researchers in the audience. In addition to giving a forum for expert practitioners to meet and share best practice, a key aim of the series is to close the gap between research and practice, establishing a feedback loop to communicate the needs of practitioners to those working in university research.
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Capacity maximising traffic signal control policies
1. NORTHMOST (12 December 2016)
Capacity-maximising
traffic signal control policies
“If you eliminate the impossible,
whatever remains, however improbable,
must be the truth.”
2. NORTHMOST (12 December 2016)
Capacity-maximising
traffic signal control policies
“If you eliminate the impossible,
whatever remains, however improbable,
must be the truth.”
(Sherlock Holmes,
Sign of the Four, 1890)
3. NORTHMOST (12 December 2016)
Capacity-maximising
traffic signal control policies
Mike Smith, Ronghui Liu, Takamasa Iryo, Tung Le, Hai Vu
The University of York, UK
ITS, University of Leeds, UK
Kobe University, Japan
Swinburne University of Technology, Melbourne, Australia
University of Monash , Melbourne, Australia
7. Modelling Signal Control and Route
Choice
Allsop, Dickson, Gartner, Smith, Van Zuylen,
Meneguzzer, Gentile, Noekel, Taale, Cantarella,
Mounce, Ke Han, Viti, Schlaich, Haupt, Lo, Rinaldi,
Cantelmo, Cascetta, Tung Le, Hai Vu, . . .
●
●
●
Previous Work
29. BASIC IDEA
DEMAND
SET D
-C
b
SUPPLY –
FEASIBLE
SET S
n(D)
-C is normal to D∩S
b is normal to S
-C = n(D) + b
-(C+b) = n(D)
-(C+b) is normal to D
P0:
30. BASIC IDEA
DEMAND
SET D
-C
b
SUPPLY –
FEASIBLE
SET S
n(D)
-C is normal to D∩S
b is normal to S
-C = n(D) + b
-(C+b) = n(D)
-(C+b) is normal to D
EQUILIBRIUM
consistent with P0
P0:
33. IS Q/G RIGHT ?
sibi Basic P0
Qi/Gi P0 with vertical queue
Qi
p/Gi THIS TALK
34. Policy: At time “t” swap green-time
towards the stage with the higher pressure
IF Pressi(t) > Pressj(t)
THEN swap some green
from stage j to stage i
35. Policy: At time “t” swap green-time
towards the stage with the higher pressure
dGi (t)/dt = Pressi(t) - Pressj(t)
dGj (t)/dt = Pressj(t) - Pressi(t)
36. Policy: At time “t” swap green-time
towards the stage with the higher pressure
dG1(t)/dt = Press1(t) – Press2(t)
dG2(t)/dt = Press2(t) – Press1(t)
37. Exact Policy: At time “t” swap green-time
to exactly equalise stage pressures
Choose G(t) so that
Press1(t)= Press2(t)
61. CONCLUSIONS:
Stated a p-evolution eqn. showing
how route-inflows, green-times and
queues evolve for all future time.
p = 1 and p ≠ 1.
62. CONCLUSIONS:
Stated a p-evolution eqn. showing
how route-inflows, green-times and
queues evolve for all future time.
p ≠ 1: FAILS to maximise capacity
p = 1: P0: maximises capacity.
63. CONCLUSIONS:
p ≠ 1: FAILS to maximise capacity
p = 1 (P0): maximises capacity.
Holmes:
All p ≠ 1 are eliminated, p = 1 or P0
remains; which must be the ONLY p
such that
“policy p is capacity maximising”
is the truth.