ABSTRACTIn many ‘smart city’ applications, congestion arises in part due to the nature of signals received by individuals from a central authority. In the model of , each agent uses one out of multiple resources at each time instant. The per-use cost of a resource depends on the number of concurrent users. A central authority has up-to-date knowledge of the congestion across all resources and uses randomisation to provide a scalar or an interval for each resource at each time. In this paper, the interval to broadcast per resource is obtained by taking the minima and maxima of costs observed within a time window of length r, rather than by randomisation. We show that the resulting distribution of agents across resources also converges in distribution, under plausible assumptions about the evolution of the population over time.
In the transportation literature, Daganzo and Sheffi @cite_49 have introduced the concept of stochastic user equilibrium, where users have considerable amounts of information, and perhaps surprising analytical powers. Subsequently, a number of variants have been proposed, e.g., @cite_31 consider robust variants and @cite_54 consider the stochastic user equilibrium with distributional uncertainty over the travel times. @cite_21 consider a stratified and risk-averse population, but only as much as a link failure is concerned. There are a number of other notions of stability, perhaps closer to our notion, inasmuch they capture the repeated nature of the problem. For example, @cite_50 introduces the notion of equilibrium as the limit of the congestion distribution if it exists. @cite_14 considers a number of notions of noisy signals and studies greedy policies and equilibria. Our approach is different from those that assign actions to agents, instead of presenting them with information and letting them make the decisions.
@cite_14 @cite_54 @cite_21 @cite_50 @cite_49 @cite_31
1998816621 2072113937 2044688536 2039423859
The problem of transporting patients or elderly people has been widely studied in literature and is usually modeled as a dial-a-ride problem (DARP). In this paper we analyze the corresponding problem arising in the daily operation of the Austrian Red Cross. This nongovernmental organization is the largest organization performing patient transportation in Austria. The aim is to design vehicle routes to serve partially dynamic transportation requests using a fixed vehicle fleet. Each request requires transportation from a patient's home location to a hospital (outbound request) or back home from the hospital (inbound request). Some of these requests are known in advance. Some requests are dynamic in the sense that they appear during the day without any prior information. Finally, some inbound requests are stochastic. More precisely, with a certain probability each outbound request causes a corresponding inbound request on the same day. Some stochastic information about these return transports is available from historical data. The purpose of this study is to investigate, whether using this information in designing the routes has a significant positive effect on the solution quality. The problem is modeled as a dynamic stochastic dial-a-ride problem with expected return transports. We propose four different modifications of metaheuristic solution approaches for this problem. In detail, we test dynamic versions of variable neighborhood search (VNS) and stochastic VNS (S-VNS) as well as modified versions of the multiple plan approach (MPA) and the multiple scenario approach (MSA). Tests are performed using 12 sets of test instances based on a real road network. Various demand scenarios are generated based on the available real data. Results show that using the stochastic information on return transports leads to average improvements of around 15 . Moreover, improvements of up to 41 can be achieved for some test instances. In the traffic assignment problem, first proposed by Wardrop in 1952, commuters select the shortest available path to travel from their origins to their destinations. We study a generalization of this problem in which competitors, who may control a nonnegligible fraction of the total flow, ship goods across a network. This type of games, usually referred to as atomic games, readily applies to situations in which the competing freight companies have market power. Other applications include intelligent transportation systems, competition among telecommunication network service providers, and scheduling with flexible machines. Our goal is to determine to what extent these systems can benefit from some form of coordination or regulation. We measure the quality of the outcome of the game without centralized control by computing the worst-case inefficiency of Nash equilibria. The main conclusion is that although self-interested competitors will not achieve a fully efficient solution from the system's point of view, the loss is not too severe. We show how to compute several bounds for the worst-case inefficiency that depend on the characteristics of cost functions and on the market structure in the game. In addition, building upon the work of Catoni and Pallotino, we show examples in which market aggregation (or collusion) adversely impacts the aggregated competitors, even though their market power increases. For example, Nash equilibria of atomic network games may be less efficient than the corresponding Wardrop equilibria. When competitors are completely symmetric, we provide a characterization of the Nash equilibrium using a potential function, and prove that this counterintuitive phenomenon does not arise. Finally, we study a pricing mechanism that elicits more coordination from the players by reducing the worst-case inefficiency of Nash equilibria. Traditionally, traffic assignment models, both for within-day static and dynamic demand, have been formulated following an equilibrium approach in which a state ensuring internal consistency between demand (flows) and costs is sought. However, equilibrium analysis is significant under some assumptions on its “representativeness” (coincidence or closeness with the actual attractor of the system) and analytical properties, such as existence, uniqueness, and stability. Moreover, transients due to modifications of demand and or supply cannot be simulated through equilibrium models, nor can a statistical description of the state of the system, i.e. means, modes, moments and, more generally, frequency distributions of flows over time be obtained. In this paper, interperiodic (day-to-day) dynamic modeling of transportation networks is addressed following two different approaches, namely deterministic and stochastic processes. In both cases several theoretical results are shown by making use of a formal framework covering most models discussed in the literature as well as some possible extensions. Most of the results reported can be extended to cover within-day dynamic models but these models are not explicitly dealt with. Within the framework of deterministic processes the relevance of day-to-day dynamic models for demand supply interaction in comparison with the traditional user equilibrium approach is discussed, and conditions for coincidence of fixed-point attractors and equilibrium states are stated. Conditions for existence and uniqueness of fixed-point attractors are proposed, generalizing and extending those presented in the literature for user equilibrium. Conditions for stability of both fixed-points and equilibrium states were formulated by making use of results from non-linear dynamic system theory. Moreover, it is possible to devise a new family of “dynamic” algorithms which simulate the system convergence to a fixed-point in order to obtain an equivalent equilibrium state, as opposed to conventional “optimisation” algorithms. In this case the fixed-point stability analysis can be viewed as a convergence analysis for the algorithms specified this way. Conditions for stochastic process regularity are proposed ensuring, among other things, existence and uniqueness of a stationary probability distribution of system states. These conditions generalize and extend results presented in the literature to a wider class of possible dynamic models. Relationships between a deterministic process, together with corresponding fixed-points or equilibrium states, and stochastic probability distribution are also briefly addressed. Finally, some numerical examples confirming theoretical results are reported for a small test network. This paper contains a quantitative evaluation of probabilistic traffic assignment models and proposes an alternate formulation. First, the concept of stochastic-user-equilibration (S-U-E) is formalized as an extension of Wardrop's user-equilibration criterion. Then, the stochastic-network-loading (S-N-L) problem (a special case of S-U-E for networks with constant link costs) is analyzed in detail and an expression for the probability of route choice which is based on two general postulates of user behavior is derived. The paper also discusses the weaknesses of existing S-N-L techniques with special attention paid to Dial's multipath method and compares them to the suggested approach. The proposed model seems reasonable and does not exhibit the inherent weaknesses of the logit model when applied to sets of routes which overlap heavily. The discussion is supported by several numerical examples on small contrived networks. The paper concludes with the discussion of two techniques that can be used to approximate the link flows resulting from the proposed model in large networks.