Asymptotic approximations of transient behaviour for day-to-day traffic models

Abstract

We consider a wide class of stochastic process traffic assignment models that capture the dayto-day evolving interaction between traffic congestion and drivers' information acquisition and choice processes. Such models provide a description of not only transient change and 'steady' behaviour, but also represent additional variability that occurs through probabilistic descriptions. They are therefore highly suited to modelling both the disturbance and subsequent 'drift' of networks that are subject to some systematic change, be that a road closure or capacity reduction, new policy measure or general change in demand patterns. In this paper we derive analytic results to probabilistically capture the nature of the transient effects following such a systematic change. This can be thought of as understanding what happens as a system moves from varying about one equilibrium state to varying about a new equilibrium state. The results capture analytically the changes over time in descriptors of the system, in terms of link flow means, variances and covariances. Formally, the analytic results hold asymptotically as approximations, as we imagine demand increasing in tandem with capacities; however, our interest is in general cases where such tandem increases do not occur, and so we provide conditions under which our approximations are likely to work well. Numerical results of applying the methods are reported on several examples. The quality of the approximations is assessed through comparisons with Monte Carlo simulations from the true underlying process.

Day-to-Day Dynamic Multivehicle Assignment: Deterministic Process Models

“…e above-described arc flow updating relation ( 16) can be combined with the arc cost updating relation (13) or (15) to specify deterministic process (DP) models for day-to-day dynamic assignment.…”

“…for given f 0 , and x 0 � c(f 0 ). e DP model (11)(12)(13)(14) can easily be rewritten as a proper Markovian DP by putting equation ( 13) into ( 15), but still keeping equation (13). e state variables of DP model (11,14) are (x k , f k ); the updating parameters are α and β; other parameters are demand flow, d, and any other parameter in the arc flow function and in the arc cost function.…”

“…with suitable initialization. e fixed-point states of both DP model (11,14) and (13,14) are equivalent to the equilibrium states as defined by FP model (9,10). Applying techniques from the theory of discrete-time nonlinear dynamic systems, the above DP models can be used to study the local stability of each fixed-point state, say whether it is an attractor.…”

“…A first unifying framework was proposed by Cantarella and Cascetta (1995) [10]. Additional details on SP are available (e.g., [11][12][13]).…”

Day-to-day dynamic traffic assignment with imperfect information, bounded rationality and information sharing

“…According to Cantarella and Watling (2016), stochastic models are more naturally associated with modelling the variability that is seen to occur in real-life systems, which are able to represent both dynamic transitions and steady-state fluctuations not seen in equilibrium models. A significant number of studies are associated with DTD traffic network modeling (Guo and Liu, 2011;Cantarella and Watling, 2016;Wang et al, 2016;Xiao and Lo, 2016;Bifulo et al, 2016;Rambha and Boyles, 2016;Zhang et al, 2018;Guo and Szeto, 2018;Watling and Hazelton, 2018).…”