Route swapping in dynamic traffic networks

Mounce, Richard; Carey, Malachy

doi:10.1016/j.trb.2010.05.005

Cited by 63 publications

(37 citation statements)

References 18 publications

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“…Mounce (2006Mounce ( , 2009, Mounce and Carey (2011) and Mounce and Smith (2007) present route-swap results which are related to those presented here. Bie and Lo (2010) have considered stability and attraction domains arising in route swap models and He et al (2010) have considered link-based models of route swapping.…”

Section: A Brief Contextsupporting

confidence: 83%

Traffic control and route choice: Capacity maximisation and stability

Smith

Liu

Mounce

2015

Transportation Research Part B: Methodological

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This paper presents idealised natural general and special dynamical models of day-to-day rerouteing and of day to day green-time response. Both green-time response models are based on the responsive control policy P 0 introduced in Smith (1979aSmith ( , b, c 1987. Several results are proved. For example, it is shown that, for any steady feasible demand within a flow model, if the general day to day re-routeing model is combined with the general day to day green-time response model then under natural conditions any (flow, green-time) solution trajectory cannot leave the region of supply-feasible (flow, green-time) pairs and costs are bounded. Throughput is maximised in the following sense.Given any constant feasible demand; this demand is met as any routeing / green-time trajectory evolves (following either the general or the special dynamical model). The paper then considers simple "pressure driven" responsive control policies, with explicit signal cycles of fixed positive duration. A possible approach to dynamic traffic control allowing for variable route choices is outlined. It is finally shown that modified Varaiya (2013) and Le at al (2013) pressure-driven responsive controls may not maximise network capacity, by considering a very simple one junction network. It is shown that (with each of these two modified policies) there is a steady demand within the capacity of the network for which there is no Wardrop equilibrium consistent with the policy. In contrast, responsive P 0 on this simple network does maximise throughput at a quasi-dynamic user equilibrium consistent with P 0 ; queues and delays remain bounded in natural dynamical evolutions in this case. It is to be expected that this P 0 result may be extended to allow for certain time-varying demands on a much wider variety of networks; to show that this is indeed the case is a challenge for the future.

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Section: A Brief Contextsupporting

confidence: 83%

Traffic control and route choice: Capacity maximisation and stability

Smith

Liu

Mounce

2015

Transportation Research Part B: Methodological

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“…Existing studies dealing with a 'dual dynamic model' (i.e. a model considering both day-to-day and within-day dynamics) include Cascetta and Cantarella (1993), Mounce (2006), Iryo (2008), Carey (2011), andFriesz et al (2011). Another alternative to equilibrium is 'tolerance-based DUO' (Szeto and Lo 2006), in which a small gap is allowed between the travel cost of a used route and the minimum travel cost.…”

Section: Summary and Discussion On Future Research On Due Solution Pmentioning

confidence: 99%

Properties of dynamic user equilibrium solution: existence, uniqueness, stability, and robust solution methodology

Iryo

2013

Transportmetrica B: Transport Dynamics

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This paper reviews studies that deal with properties of dynamic user equilibrium (DUE) solutions to understand the extent to which they have been resolved in past studies and indicate theoretical problems that remain to be addressed in future research. DUE assignment is an equilibrium-based methodology for dynamic traffic assignment. In conventional equilibriumbased static traffic assignment, the four desirable properties of solutions -existence, uniqueness, stability of solutions, and the existence of a robust solution methodology -are all guaranteed. These properties must be ensured for planners to obtain a reliable solution for equilibriumbased assignment. Meanwhile, for DUE assignment, although some of these properties have been proved, many issues regarding these properties remain unresolved. This paper reviews studies that deal with these properties to understand how far they have been investigated and discusses what is required from future research to improve the robustness of DUE assignment.

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“…Also, ( ) A similar method is proposed in Carey and Ge (2012) to search for a route-choice DUE solution by swapping flows between each pair of paths; as implied in this reference, the above method may have other forms, for example we can remove departure rates from time intervals in proportion to their deviation ( ) ′ − 1 nk n g g C C from the time interval with the minimum generalised travel cost and reassign all of these removed departure rates to the time interval with the minimum generalised travel cost. Mounce and Carey (2011) investigates the convergence of the path-oriented swapping method and the speed of convergence.…”

Section: Methodsmentioning

confidence: 99%

Investigating boundary effects of congestion charging in a single bottleneck scenario

Stewart

Liu

et al. 2015

Transport

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Abstract. Many congestion charging projects charge traffic only within part of a day with predetermined congestion tolls. Demand peaks have been witnessed just around the time when the charge jumps up or down. Such peaks may not be desirable, in particular (a) when the resulting peaks are much higher than available capacities; (b) traffic speeding up to get into the charging zone causes more incidents just before the toll rises up to a higher level; or (c) traffic slowing down or parking on the roadside decreases road traffic throughput just before the toll falls sharply. We term these types of demand peaks 'boundary effects' of congestion charging. This paper investigates these effects in a bottleneck scenario and aims to design charging schemes that reduce undesired demand peaks. For this purpose, we observe and analyse the boundary effects utilising a bottleneck model under three types of toll profiles that are indicative of real charging schemes. The first type maintains a constant toll across the charging period, the second type allows the toll to increase from zero to a given maximum level and then decrease back to zero and the third type allows the toll to rise from zero to a given maximum level, remain at this level for a fixed period and then fall down to zero. This investigation shows that all three types of toll profiles can produce greater boundary peak demands than the bottleneck capacity. A significant contribution of this work is that instead of designing an optimal traffic congestion pricing scheme we analyse how existing sub-optimal congestion pricing schemes could be improved and suggest how observed problems may be overcome. Hence, we propose a set of extra requirements to supplement existing principles or requirements for design and implementation of congestion charging, which aim to reduce the adverse consequences of boundary effects. Concluding remarks are made on implications of this investigation for the improvement of existing congestion charging projects and for future research. Keywords: bottleneck models; congestion charging; boundary issues. Notes: Current paper is an entirely updated version of our earlier paper: Ge, Y.-E.; Stewart, K. 2010. Investigating boundary issues arising from congestion charging in a bottleneck scenario, in C. M. J. Tampère, F. Viti, L. H. Immers (Eds.). New Developments in Transport Planning: Advances in Dynamic Traffic Assignment, 303-327. http://dx.doi.org/10.4337/9781781000809.00025 In this new version, we have rewritten the introductory section. Secondly, we are proposing a set of extra requirements for road traffic congestion pricing design and implementation in a newly-added section. Thirdly, three new tables have been generated and the data in them are used to support our analysis while four new figures are added to show the advantages of the adopted bottleneck model over the existing ones. Besides, we significantly improved the presentation and analysis of numerical results as well as corrected the errors and typos in the earlier version througho...

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Route swapping in dynamic traffic networks

Cited by 63 publications

References 18 publications

Traffic control and route choice: Capacity maximisation and stability

Traffic control and route choice: Capacity maximisation and stability

Properties of dynamic user equilibrium solution: existence, uniqueness, stability, and robust solution methodology

Investigating boundary effects of congestion charging in a single bottleneck scenario

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