Optimization of traffic sensor location for complete link flow observability in traffic network considering sensor failure

The full link flow observability problem is to identify the minimum set of traffic sensors to be installed in links in a road traffic network. The sensors are used to both monitor the flow of observed links and to provide flow information for the link flow inference of unobserved links. Unavoidably, the traffic sensors deployed in a traffic network are subject to failure which leads to missing the link flow observation of observed links as well as the inability to infer the link flow of unobserved links. This study aims to identify the minimum set of links in a traffic network to be instrumented with two different types of counting sensors (basic and advanced sensors) to reach full link flow observability while minimizing the effect of sensor failure on the link flow inference of unobserved links. Mathematically, we formulate two objective functions including min-max and min-sum functions. The first function attempts to minimize the maximum effect of sensor failure on the link flow inference of unobserved links while the second one minimizes the expected number of unobserved links where flow cannot be inferred due to the failure of sensors. We select the genetic algorithm (GA) as a well-known heuristic to solve the proposed optimization model. The results recommend minimizing the number of sensors required for the link flow inference of each unobserved link as well as installing advanced sensors on links involved in the link flow inference of multiple unobserved links. We also develop a new objective function to reflect that links in a traffic network can be either minor or major roads with different levels of importance. The results suggest installing more advanced sensors on the major roads as well as minimizing the number of major roads included in the set of unobserved links. Concerning the availability of route flow information in a network, we consider the effect of this information on evaluating the sensor deployment in a network. To maintain full link flow observability of a traffic network if any sensor fails, we study the location and type of additional sensors introduced as redundant sensors, which are more than the minimum required for full link flow observability. Finally, we discuss the applicability of the proposed model for the partial observability problem in which the full link flow observability conditions are not satisfied.