Convergence in a continuous dynamic queueing model for traffic networks

Mounce, Richard

doi:10.1016/j.trb.2005.10.004

Cited by 75 publications

(47 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…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: 82%

Traffic control and route choice: Capacity maximisation and stability

Smith

Liu

Mounce

2015

Transportation Research Part B: Methodological

View full text Add to dashboard Cite

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.

show abstract

Section: A Brief Contextsupporting

confidence: 82%

Traffic control and route choice: Capacity maximisation and stability

Smith

Liu

Mounce

2015

Transportation Research Part B: Methodological

View full text Add to dashboard Cite

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

“…Other route swap algorithms have been considered by Cascetta (1989), Smith and Wisten (1995), Bellei et al (2005), Huang and Lam (2002), Peeta and Yang (2003), Nie and Zhang (2005), Nie (2010), Mounce (2006Mounce ( , 2009, Mounce and Carey (2011) and Mounce and Smith (2007). None utilise paired alternative segments.…”

Section: Overview and Contributions Of This Papermentioning

confidence: 99%

Route choice and traffic signal control: A study of the stability and instability of a new dynamical model of route choice and traffic signal control

Liu

Smith

2015

Transportation Research Part B: Methodological

View full text Add to dashboard Cite

This paper presents a novel idealised dynamical model of day to day traffic re-routeing (as traffic seeks cheaper routes) and proves a stability result for this dynamical model. (The dynamical model is based on swapping flow between paired alternative segments (these were introduced by Bar Gera (2010)) rather than between routes.) It is shown that under certain conditions the dynamical system enters a given connected set of approximate equilibria in a finite number of days or steps. This proof allows for saturation flows which act as potentially active flow constraints. The dynamical system involving paired alternative segment swaps is then combined with a novel green-time-swapping rule; this rule swaps green-time toward more pressurised signal stages. It is shown that if (i) the delay formulae have a simple form and (ii) the "pressure" formula fits the special control policy P 0 (see Smith, 1979a, b), then the combined flow-swapping / green-time-swapping dynamical model also enters a given connected set of approximate consistent equilibria in a finite number of steps. Computational results confirm, in a simple network, the positive P 0 result and also show, on the other hand, that such good behaviour may not arise if the equi-saturation control policy is utilized. The dynamical models described here do not represent blocking back effects.

show abstract

Convergence in a continuous dynamic queueing model for traffic networks

Cited by 75 publications

References 13 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

Route choice and traffic signal control: A study of the stability and instability of a new dynamical model of route choice and traffic signal control

Contact Info

Product

Resources

About