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Equilibrium in capacitated network models with queueing delays, queue-storage, blocking back and control
Smith, Mike J.; Huang, Wei; Viti, Francesco
2013In Procedia Social and Behavioral Sciences, 80, p. 860-879
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Keywords :
Link-based traffic assignment; Capacity-constrained equilibrium; Elastic Demand; Queueing; Blocking Back
Abstract :
[en] This paper considers a steady-state, link-based, fixed (or inelastic) demand equilibrium model with explicit link-exit capacities, explicit bottleneck or queuing delays and explicit bounds on queue storage capacities. The (spatial queueing) model at the heart of this equilibrium model takes account of the space taken up by queues both when there is no blocking back and also when there is blocking back. The paper shows in theorem 1 that a feasible traffic assignment model has an equilibrium solution provided prices are used to impose capacity restrictions and utilises this result to show that there is an equilibrium with the spatial queueing model, provided queue-storage capacities are sufficiently large. Other results are obtained by changing the variables and sets in theorem 1 suitably. These results include: (1) existence of equilibrium results (in both a steady state and a dynamic context) which allow signal green-times to respond to prices and (2) an existence of equilibrium result which allow signal green-times to respond to spatial queues; provided this response follows the P0 control policy in Smith (1979, 1987). These results show that under certain conditions the P0 control policy maximises network capacity. The spatial queueing model is illustrated on a simple network. Finally the paper includes elastic demand; this is necessary for long-run evaluations. Each of the steady state models here may be thought of as a stationary solution to the dynamic assignment problem either with or without blocking back.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Smith, Mike J.
Huang, Wei
Viti, Francesco  ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit
External co-authors :
yes
Language :
English
Title :
Equilibrium in capacitated network models with queueing delays, queue-storage, blocking back and control
Publication date :
2013
Event name :
20th International Symposium on Transportation and Traffic Theory (ISTTT 2013)
Event date :
from 16-07-2013 to 19-07-2013
Audience :
International
Journal title :
Procedia Social and Behavioral Sciences
ISSN :
1877-0428
Publisher :
Elsevier, Amsterdam, Netherlands
Volume :
80
Pages :
860-879
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBilu :
since 01 November 2013

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