Blocking back; Capacity-constrained equilibrium; Merge control; Queueing; Upstream gating; Blockings; Constrained equilibriums; Down-stream; Network Capacity; Simple networks; Civil and Structural Engineering; Automotive Engineering; Transportation; Management Science and Operations Research
Abstract :
[en] This paper considers a simple network with a merge and a downstream bottleneck, which corresponds to a very congested part of the City of York road network - Gillygate. We focus on “upstream-gating” control strategies which hold traffic back at traffic signals just ahead of the merge to prevent the formation of a queue at a downstream bottleneck; and we also consider different ways of further, additionally, controlling the two inflows to the merge. We show, by considering the simple network, that if the added upstream merge-control uses only flows to control the two approaches to the merge then equilibrium may not exist. For example, with the “zipper” rule (which equalises the two inflows at the merge) an equilibrium cannot exist for certain feasible demands on this network. On the other hand, we show that adding upstream merge-control which equalises the two delays felt at the merge allows an equilibrium for all feasible demands on this network, and so maximises the network capacity, notwithstanding the upstream gating. This suggests that, in general, delays should probably be used to control merges and downstream queues, rather than only flows, if network capacity is to be maximised. This observation may help the design of good control strategies, using both flows and delays, for upstream-gating designed to remove or reduce queues at specific downstream locations. The equilibrium analysis in our example is supported by (i) a dynamic analysis allowing for the dynamic growth of queues in the example network and (ii) real-life results of upstream-gating applied to Gillygate in York (UK) which provided motivation for this paper. The analysis here makes reasonable allowance for the spatial extent of queues but does not consider within-cycle or cycle-to-cycle queueing dynamics.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Smith, Michael J.; Department of Mathematics, University of York, United Kingdom
VITI, Francesco ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Engineering (DoE)
Huang, Wei; School of Intelligent Systems Engineering, Sun Yat-sen University, China
Mounce, Richard; University of Aberdeen, United Kingdom
External co-authors :
yes
Language :
English
Title :
Upstream-gating merge-control for maximising network capacity: With an application to urban traffic management
Publication date :
October 2023
Journal title :
Transportation Research. Part C, Emerging Technologies
We acknowledge substantial inputs to this paper by referees who suggested, (a) the addition of the proof at the end of section 3 and, (b) several other corrections, additions and changes. One of the main additions is section 5 which includes some dynamics, and the main correction, in the graph in Fig. 6, shows that the performance of the biased equi-delay policy (f) appears to be much better than we initially thought. This paper has been very carefully designed to take some reasonable account of the spatial extent of queues, but this paper does not seek to represent within-cycle or cycle-to-cycle queue dynamics. A referee has suggested that the work presented here would profit substantially from extensions which represent within-cycle queue dynamics. We agree and we believe that this represents a challenging opportunity for the future.
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