A mixed integer linear programming model for dynamic route guidance

Abstract

One of the major challenges facing ITS (Intelligent Transportation Systems) today is to offer route guidance to vehicular traffic so as to reduce trip time experienced. In a cooperative route guidance system, the problem becomes one of assigning routes to vehicles departing at given times from a set of origins to a set of destinations so as to minimize the average trip time experienced (a so-called system optimal criterion) Since the time to traverse a link will depend upon traffic volume encountered on that link, link times are dynamic. The complex interaction resulting between objective function and constraints makes the dynamic problem significantly more difficult to formulate and solve than the static version. We present a mixed integer linear programming * This work was supported in part by the Intelligent Transportation Systems Research Center of Excellence at the University of Michigan 1 formulation of the problem which is formally derived from a set of traffic flow assumptions. Principal among these is the simplifying assumption that vehicles upon entering a link assume the speed that traffic would attain were the traffic volume encountered on that link in steady-state. The integer variables correspond to selection of vehicle capacity constraints on the link while the continuous variables correspond to selection of vehicle routes. Implicit within this MILP formulation of the dynamic traffic assignment problem is therefore a decomposition of the problem that results in a conventional capacitated linear programming network flow problem. A small illustrative subnetwork extracted from the city of Sioux Falls is solved to optimality by IBM's OSL Branch-and-Bound algorithm.

Hybrid Vehicle-Centric Route Guidance 1

“…Kaufman et al [30] describes another mathematical programming method for the systemoptimal problem in which arc travel times in the network depend only on arc volume and queue spillback is not modelled. Other traffic modeling assumptions are made regarding the FIFO behavior of network arcs.…”

Hierarchical route choice control for baggage handling systems

“…[2], [3]. But, in our case we do not deal with a shortest-path or shortest-time problem, since we need the bags at their corresponding end point within a given time window.…”

Discrete-time dynamic traffic assignment models with periodic planning horizon: system optimum

“…Since Merchant and Nemhauser (see, [30] and [31]) first proposed their model in 1978, there have been a number of papers (see, e.g., [13], [6], [44], [14], [24], [23], [48], [17], [27], [25], and [42]) discussing the variational inequalities or mathematical programming formulations for the dynamic traffic assignment problem with the assumption that the planning horizon is a set of discrete points instead of a continuous interval. Many of these papers use a dynamic or time-expanded network (see, e.g., [1]) to simultaneously capture the topology of the transportation network and the evolution of traffic over time.…”

“…First, some (e.g., [30], [13], [23], [6], [48], [25], [21]) seek a system optimal solution and others (e.g., [24], [44], [14], and [17]) compute a user equilibrium instead. The other factor is the travel cost function used by these models.…”

“…Similar to Carey and Srinivasan [12], Carey and Subrahmanian [13], Carey [6], Chen and Hsueh [14] and Koufman et al [25], the model in this paper is based on the time-expanded network. However, instead of assuming that the network is empty at the beginning or at the end, this paper treats the planning horizon as a circular interval instead of linear.…”