Numerical Stability of Path-based Algorithms For Traffic Assignment

In this paper we study numerical stability of path-based algorithms for the traffic assignment problem. These algorithms are based on decomposition of the original problem into smaller sub-problems which are optimised sequentially. Previously, path-based algorithms were numerically tested only in the setting of moderate requirements to the level of solution precision. In this study we analyse convergence of these methods when the convergence measure approaches machine epsilon of IEEE double precision format. In particular, we demonstrate that the straightforward implementation of one of the algorithms of this group (projected gradient) suffers from loss of precision and is not able to converge to highly precise solution. We propose a way to solve this problem and test the proposed adjusted version of the algorithm on various benchmark instances

A Lagrangian discretization multiagent approach for large-scale multimodal dynamic assignment

This paper develops a Lagrangian discretization multiagent model for large-scale multimodal simulation and assignment. For road traffic flow modeling, we describe the dynamics of vehicle packets based on a macroscopic model on the basis of a Lagrangian discretization. The metro/tram/train systems are modeled on constant speed on scheduled timetable/frequency over lines of operations. Congestion is modeled as waiting time at stations plus induced discomfort when the capacity of vehicle is achieved. For the bus system, it is modeled similar to cars with different speed settings, either competing for road capacity resources with other vehicles or moving on separated bus lines on the road network. For solving the large-scale multimodal dynamic traffic assignment problem, an effective-path-based cross entropy is proposed to approximate the dynamic user equilibrium. Some numerical simulations have been conducted to demonstrate its ability to describe traffic dynamics on road network.multimodal transportation systems; Lagrangian discretization; traffic assignment; multiagent systems

Scheduling strategies for LTE uplink with flow behaviour analysis

Long Term Evolution (LTE) is a cellular technology developed to support\ud diversity of data traffic at potentially high rates. It is foreseen to extend the capacity and improve the performance of current 3G cellular networks. A key\ud mechanism in the LTE traffic handling is the packet scheduler, which is in charge of allocating resources to active flows in both the frequency and time dimension. In this paper we present a performance comparison of two distinct scheduling schemes for LTE uplink (fair fixed assignment and fair work-conserving) taking into account both packet level characteristics and flow level dynamics due to the random user behaviour. For that purpose, we apply a combined analytical/simulation approach which enables fast evaluation of performance measures such as mean flow transfer times manifesting the impact of resource allocation strategies. The results show that the resource allocation strategy has a crucial impact on performance and that some trends are observed only if flow level dynamics are considered

A Coevolutionary Particle Swarm Algorithm for Bi-Level Variational Inequalities: Applications to Competition in Highway Transportation Networks

A climate of increasing deregulation in traditional highway transportation, where the private sector has an expanded role in the provision of traditional transportation services, provides a background for practical policy issues to be investigated. One of the key issues of interest, and the focus of this chapter, would be the equilibrium decision variables offered by participants in this market. By assuming that the private sector participants play a Nash game, the above problem can be described as a Bi-Level Variational Inequality (BLVI). Our problem differs from the classical Cournot-Nash game because each and every player’s actions is constrained by another variational inequality describing the equilibrium route choice of users on the network. In this chapter, we discuss this BLVI and suggest a heuristic coevolutionary particle swarm algorithm for its resolution. Our proposed algorithm is subsequently tested on example problems drawn from the literature. The numerical experiments suggest that the proposed algorithm is a viable solution method for this problem