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We study a double-ended queue consisting of two classes of customers. Whenever there is a pair of customers from both classes, they are matched and leave the system. The matching is instantaneous following the first-come-first-match principle. If a customer cannot be matched immediately, he/she will stay in a queue. We also assume customers are impatient with generally distributed patience times. Under suitable heavy traffic conditions, we establish simple linear asymptotic relationships between the diffusion-scaled queue length process and the diffusion-scaled offered waiting time processes and show that the diffusion-scaled queue length process converges weakly to a diffusion process that admits a unique stationary distribution. [ABSTRACT FROM AUTHOR]

Arrival processes to service systems often display fluctuations that are larger than anticipated under the Poisson assumption, a phenomenon that is referred to as overdispersion. Motivated by this, we analyze a class of discrete-time stochastic models for which we derive heavy-traffic approximations that are scalable in the system size. Subsequently, we show how this leads to novel capacity sizing rules that acknowledge the presence of overdispersion. This, in turn, leads to robust approximations for performance characteristics of systems that are of moderate size and/or may not operate in heavy traffic. [ABSTRACT FROM AUTHOR]

In a traffic-aware route search (TARS), the user provides start and target locations and sets of search terms. The goal is to find the fastest route from the start location to the target via geographic entities (points of interest) that correspond to the search terms, while taking into account variations in the travel speed due to changes in traffic conditions, and the possibility that some visited entities will not satisfy the search requirements. A TARS query may include temporal constraints and order constraints that restrict the order by which entities are visited. Since TARS generalizes the Traveling-Salesperson Problem, it is an NP-hard problem. Thus, it is unlikely to find a polynomial-time algorithm for evaluating TARS queries. Hence, we present in this paper three heuristics to answer TARS queries-a local greedy approach, a global greedy approach and an algorithm that computes a linear approximation to the travel speeds, formulates the problem as a Mixed Integer Linear Programming (MILP) problem and uses a solver to find a solution. We provide an experimental evaluation based on actual traffic data and show that using a MILP solver to find a solution is effective and can be done within a limited running time in many real-life scenarios. The local-greedy approach is the least effective in finding a fast route, however, it has the best running time and it is the most scalable. [ABSTRACT FROM AUTHOR]

Daganzo’s criticisms of second-order fluid approximations of traffic flow [C. Daganzo, Transpn. Res. B. 29, 277 (1995)] and Aw and Rascle’s proposal how to overcome them [A. Aw, M. Rascle, SIAM J. Appl. Math. 60, 916 (2000)] have stimulated an intensive scientific activity in the field of traffic modeling. Here, we will revisit their arguments and the interpretations behind them. We will start by analyzing the linear stability of traffic models, which is a widely established approach to study the ability of traffic models to describe emergent traffic jams. Besides deriving a collection of useful formulas for stability analyses, the main attention is put on the characteristic speeds, which are related to the group velocities of the linearized model equations. Most macroscopic traffic models with a dynamic velocity equation appear to predict two characteristic speeds, one of which is faster than the average velocity. This has been claimed to constitute a theoretical inconsistency. We will carefully discuss arguments for and against this view. In particular, we will shed some new light on the problem by comparing Payne’s macroscopic traffic model with the Aw-Rascle model and macroscopic with microscopic traffic models. [ABSTRACT FROM AUTHOR]

We investigate the properties of travel times when the latter are derived from traffic-flow models. In particular we consider exit-flow models, which have been used to model time-varying flows on road networks, in dynamic traffic assignment (DTA). But we here define the class more widely to include, for example, models based on finite difference approximations to the LWR (Lighthill, Whitham and Richards) model of traffic flow, and 'large step' versions of these. For the derived travel times we investigate the properties of existence, uniqueness, continuity, first-in-first-out (FIFO), causality and time-flow consistency (or intertemporal consistency). We assume a single traffic type and assume that time may be treated as continuous or as discrete, and for each case we obtain conditions under which the above properties are satisfied, and interrelations among the properties. For example, we find that FIFO is easily satisfied, but not strict causality, and find that if we redefine travel time to ensure strict causality then we lose time-flow consistency, and that neither of these conditions is strictly necessary or sufficient for FIFO. All of the models can be viewed as an approximation to a model that is continuous in time and space (the LWR model), and it seems that any loss of desirable properties is the price we pay for using such approximations. We also extend the exit-flow models and results to allow ‘inhomogeneity’ over time (link capacity or other parameters changing over time), and show that FIFO is still ensured if the exit-flow function is defined appropriately. [ABSTRACT FROM AUTHOR]