Locating Traffic Sensors on a Highway Network Models and Algorithms

This paper considers the problem of finding optimal sensor locations on a traffic network with the goal of characterizing system use overall. The problem is studied for two practical scenarios. In the first scenario, it is assumed that there is a given number of sensors (p) to be located on the highway network. In this context, the problem is to find a collection of p locations among a given collection of candidate locations. In the second scenario, it is assumed that there is a cost (c(i)) associated with installing a sensor at each candidate location i and a total budget b. In this context, the problem is to find a collection of locations that provide the best possible characterization given the budget constraint. A metric is proposed for evaluating a potential solution, and then appropriate mathematical models are proposed for solving the problem for each scenario. It is shown that the budget-constrained problem is an extension of the well-known p-median problem. A new Lagrangian heuristic algorithm is presented for solving large instances of this problem when a budget constraint is imposed. A comprehensive computational experiment is used to demonstrate that the Lagrangian heuristic algorithm provides solutions for large-scale networks within reasonable execution times. Examples are based on locating weigh-in-motion sensors on a large-scale highway network.