A splitting rate model of traffic re-routeing and traffic control

Smith, Mike; Mounce, Richard

doi:10.1016/j.sbspro.2011.04.520

Cited by 33 publications

(39 citation statements)

References 31 publications

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“…instantaneous shortest paths, system optimum vs. user equilibrium). As a result, although new researches (e.g., Mahut and Florian, 2008;Smith and Mounce, 2011;Ramadurai and Ukkusuri, 2011) are trying to exploit some of the ideas that allowed a relevant improvement in the state-of-the-practice for static assignment (e.g. Dial, 2006;, fixed-point-like formulations, with their poor mathematical properties, and MSA (Method of Successive Averages) algorithms, with their slow convergence patterns, still seem to dominate the panorama of DTA models today (an up-to-date review of some academic and commercial software available for real-life applications can be found in Barcelo, 2010).…”

Section: Background and Motivationmentioning

confidence: 99%

Using the General Link Transmission Model in a Dynamic Traffic Assignment to Simulate Congestion on Urban Networks

Gentile

2015

Transportation Research Procedia

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This article presents two new models of Dynamic User Equilibrium that are particularly suited for ITS applications, where the evolution of vehicle flows and travel times must be simulated on large road networks, possibly in real-time. The key feature of the proposed models is the detail representation of the main congestion phenomena occurring at nodes of urban networks, such as vehicle queues and their spillback, as well as flow conflicts in mergins and diversions. Compared to the simple word of static assignment, where only the congestion along the arc is typically reproduced through a separable relation between vehicle flow and travel time, this type of DTA models are much more complex, as the above relation becomes non-separable, both in time and space. Traffic simulation is here attained through a macroscopic flow model, that extends the theory of kinematic waves to urban networks and non-linear fundamental diagrams: the General Link Transmission Model. The sub-models of the GLTM, namely the Node Intersection Model, the Forward Propagation Model of vehicles and the Backward Propagation Model of spaces, can be combined in two different ways to produce arc travel times starting from turn flows. The first approach is to consider short time intervals of a few seconds and process all nodes for each temporal layer in chronological order. The second approach allows to consider long time intervals of a few minutes and for each sub-model requires to process the whole temporal profile of involved variables. The two resulting DTA models are here analyzed and compared with the aim of identifying their possible use cases. A rigorous mathematical formulation is out of the scope of this paper, as well as a detailed explanation of the solution algorithm. The dynamic equilibrium is anyhow sought through a new method based on Gradient Projection, which is capable to solve both proposed models with any desired precision in a reasonable number of iterations. Its fast convergence is essential to show that the two proposed models for network congestion actually converge at equilibrium to nearly identical solutions in terms of arc flows and travel times, despite their two diametrical approaches wrt the dynamic nature of the problem, as shown in the numerical tests presented here.

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Section: Background and Motivationmentioning

confidence: 99%

Using the General Link Transmission Model in a Dynamic Traffic Assignment to Simulate Congestion on Urban Networks

Gentile

2015

Transportation Research Procedia

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“…The capacity maximising effect arises because both models utilise the P 0 signal control policy. This policy has been studied previously (see Smith (1979aSmith ( , b, c, 1987, Smith et al (1987), Smith and Ghali (1990), Smith and van Vuren (1993), Smith and Mounce (2011), Smith (2015) and Liu and Smith (2015). Both the performance and stability of the re-routeing -control interactions is considered.…”

Section: It Is Importantmentioning

confidence: 99%

Traffic Control and Route Choice; Capacity Maximization and Stability

Smith

Liu

Mounce

2015

Transportation Research Procedia

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This paper presents idealised natural general and special dynamical models of day-to-day re-routeing and of day to day greentime 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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“…Taking the settings into (11), we have the recurrence function of x as (Smith 1984;Smith and Mounce 2011):…”

Section: Example 1 Dynamical Traffic System With Due (Lo and Bie 2006mentioning

confidence: 99%

“…Different from fixed-time control, Smith and van Vuren (1993) proved that convergence exist only for a few control policies. Moreover, traffic assignment and signal control dynamics may become unstable and unpredictable under certain traffic assignment models (Smith and Mounce 2011). Besides, theoretical models that consider signal control and traffic assignment can be also found in some other published works, such as Yang and Yagar (1995), Yang (1996), Meneguzzer (1997.…”

Section: The Joint Dynamical System Of Route Choice and Signal Controlmentioning

confidence: 99%

“…Besides the works mentioned above, Smith (2011) extended his traffic assignment model to include responsive signal control, as illustrated in Fig. 5 below Smith and Mounce (2011) considered that traffic signal is adjusted right after traffic is assigned (the inner dashed box). This implies that the signal controller has perfect forecast of traffic arrivals on the day and determines the green allocations accordingly.…”

Section: Modeling Adaptive Signal Control In the Joint Dynamical Trafmentioning

confidence: 99%

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Combined Route Choice and Adaptive Traffic Control in a Day-to-day Dynamical System

Lin

2014

Netw Spat Econ

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We formulate a joint dynamical traffic system that encompasses both route choice and traffic control in which the signal controller interacts with and adapts to the route choices of travelers, and vice versa. Travelers' route choice dynamics are captured by a recurrence function, which governs the system evolution from day to day. Traffic control also adjusts its plan from day to day in response to the route choices of travelers. We show that this joint dynamical system has a set of fixed points in which both the user equilibrium is achieved and the traffic signal converges to a fixed-time plan. We address equilibrium stability and convergence of this joint dynamical system through analyzing the Jacobian matrix associated with each fixed point. We demonstrate the attraction domains of this joint problem and illustrate their importance and relevance for designing adaptive traffic control through some numerical examples.

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A splitting rate model of traffic re-routeing and traffic control

Cited by 33 publications

References 31 publications

Using the General Link Transmission Model in a Dynamic Traffic Assignment to Simulate Congestion on Urban Networks

Using the General Link Transmission Model in a Dynamic Traffic Assignment to Simulate Congestion on Urban Networks

Traffic Control and Route Choice; Capacity Maximization and Stability

Combined Route Choice and Adaptive Traffic Control in a Day-to-day Dynamical System

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