Locating Traffic Sensors on a Highway Network: Models and Algorithms

44 We consider the problem of finding optimal sensor locations on a traffic network so as to characterize 45 system use overall. We study the problem under two practical scenarios. In the first scenario, we assume 46 there is a given number of sensors (p) that we need to locate on the highway network. In this context, the 47 problem is to find a collection of p locations among a given collection of candidate locations. In the 48 second scenario, we assume that there is a cost (ci) associated with installing a sensor at each candidate 49 location i, and a total budget b. In this context, the problem is to find a collection of locations that provide 50 the best possible characterization given the budget constraint. We propose a metric to evaluate a potential 51 solution and then propose appropriate mathematical models for solving the problem for each scenario. We 52 show that the budget-constrained problem is an extension of the well-known p-median problem. A new 53 Lagrangian heuristic algorithm is presented to solve large instances of this problem where a budget 54 constraint is imposed. Through a comprehensive computational experiment, we demonstrate that the 55 Lagrangian heuristic algorithm provides solutions for large-scale networks within reasonable execution 56 times. Examples are based on locating weigh-in-motion (WIM) sensors on a large-scale highway 57 network. 58 59 60 INTRODUCTION 61 Despite today’s advances in instrumentation technology, it is still a challenge to find cost-effective ways 62 to create observability for highway networks. Much of the US highway network is still not instrumented. 63 For example, no one knows how many vehicles traverse most of the network segments each day let alone 64 the number of trucks. Yet good information is key to effective and successful network management. The 65 asset condition is driven by use, and resource allocation decisions are affected by relative use and 66 deterioration rates, so having defensible and effective information about asset condition is critical for 67 responsible fiscal management and refurbishment planning. Half of the data collection focuses on asset 68 condition and rates of deterioration. The other half focuses on use and use patterns. This paper focuses on 69 the latter, but both are critically important. 70 For most of the highway network, a spectrum of information about the traffic volume and loads, 71 including vehicle counts, vehicle classifications, axle loads, and gross vehicle weight is needed to 72 determine the use rate. In the context of monitoring traffic flows (volume), available literature breaks 73 down into three categories: link flow estimation (1-3), origin–destination (OD) matrix estimation (4-9), 74 and path flow estimation (10). While significant progress has been made on formulating and solving 75 sensor location problems that estimate traffic flows, not much attention has been focused on monitoring 76 traffic loads. Yet estimation of these axle loads is of great importance in developing prudent capital and 77 operating budgets for the maintenance of pavements and bridges. It has been shown that non-truck 78 vehicles have negligible effect on pavement deterioration and bridge damage (10). Therefore, we will 79 focus on truck axle loadings for this research. 80 The focus of this paper is on locating sensors that are particularly effective in measuring axle load data 81 (mainly truck axle load data). Among available surveillance systems, weight-in-motion (WIM) sensors 82 are finding increasingly widespread use in highway network management due to their capability in 83 collecting comprehensive range of traffic data including volume and loads data (11-18). 84 If WIM sensors were cheap and exhaustive deployment was easy, optimal placement of the sensors 85 would be irrelevant. WIM sensors, however, require a controlled operating environment (such as a strong, 86 smooth, and level pavement), and costly setup and calibration equipment. Hence, full instrumentation of 87 the network is still cost prohibitive and technologically challenging. Under these conditions a reasonable 88 alternative would be to install WIM sensors at a limited number of locations on the network and to infer 89 from them the traffic load data (more specifically, the axle load data) for the entire network. Several 90 questions arise in this context: 91 92 1. How do we determine the locations of the WIM sensors for monitoring traffic on the network? 93 TRB 2013 Annual Meeting Paper revised from original submittal.