Modeling the effect of sensor failure on the location of counting sensors for origin-destination (OD) estimation

The network sensor location problem (NSLP) for origin-destination (OD) estimation identifies the optimal locations for sensors to estimate the vehicular flow of OD pairs in a road network. Like other measurement apparatuses, these sensors are subject to failure, which can affect the reliability of the OD estimations. In this paper, we propose a novel model that allows us to solve the NSLP for OD demand estimation by identifying the most reliable locations to install sets of sensors with consideration for a nonhomogeneous Poisson process to account for time-dependent sensor failure. The proposed model does not rely on the assumption that true OD demand information is known. We introduce two separate objective functions to minimize the maximum possible information loss (MPIL) associated with OD demand on sensor-equipped links and OD pairs during the lifetimes of the sensors. Both objective functions are formulated to incorporate the possibility of sensor failure into the calculated OD demands. We use stochastic user equilibrium (SUE) to address the stochasticity of traffic route selection. We then employ the weighted sums method (WSM) and an epsilon-constraint to incorporate the objective functions into an integrated formulation. Two sensor types with different time-dependent failure rates are considered to identify the optimal locations for sets of sensors for OD demand estimation purposes while addressing the available budget constraints. We also address the problem of scheduled/routine maintenance of existing sensors by introducing an additional sensor deployment phase that focuses on maintaining the reliability of information by repairing or replacing failed sensors, installing additional sensors or a combination of both. The numerical results from the proposed model demonstrate how the deployment of more advanced sensors with lower failure rates can effectively improve the reliability of the information obtained from sensors. We also evaluate the use of different weights for the WSM's objective functions to explore alternative combinations of sensor configurations. The introduction of additional sensors to a network shows that the decision between repairing failed sensors and installing new sensors is highly dependent on the available budget and the failed sensors' locations.