Sensor location models with reliable optimal solution for the observation of origin–destination matrix and route flows

Origin–destination matrix (ODM) is a key element in transportation studies. The emergence of new ITS technologies like Automatic Vehicle Identification (AVI) sensors makes the ODM observation problem more interesting in recent decades. However, sensors are subject to failure in reality which highlights the sensor failure phenomenon as a significant issue in real-case problems. This study intends to include the sensor failure phenomenon in AVI Sensor Location Model (SLM) for reliable observation of ODM and route flows. While reliability and cost are usually two conflicting objectives, we try to answer the following question “Is it possible to improve reliability without increasing the cost and only by changing sensor deployment?”. In addressing this study question, first, it is shown that the solution of recent AVI SLMs are not unique. Second, we show that the reliability level of multiple optimal solutions is not the same. Third, two Mixed Integer Linear Programming (MILP) AVI SLMs for reliable observation and parital observation of ODM/route flows are developed considering the sensor failure phenomenon. The models are formulated such that their solutions are selected from the set of multiple optimal solutions. Fourth, a linear surrogate term for reliability is introduced and mathematically proven to be included in the proposed models. Finally, the applicability of the proposed models is examined on several middle-scale networks and a real-size network. Furthermore, a heuristic algorithm is customized to solve the models for the real-size network. The results suggest that there might be alternative sensor deployment strategies with the same number of sensors as in the optimal solution but with higher level of reliability for ODM/route flows observation.