Fare inspection patrolling under in-station selective inspection policy

A patrolling strategy that defines fare inspection frequencies on a proof-of-payment transportation system is operationally useful to the transit authority when there is a mechanism for its practical implementation. This study addresses the operational implementation of a fare inspection patrolling strategy under an in-station selective inspection policy using an unpredictable patrolling schedule, where the transit authority select a patrolling schedule each day with some probability. The challenge is to determine the set of patrolling schedules and their respective probabilities of being selected whose systematic day-to-day application matches the inspection frequencies that inhibit the action of opportunistic passengers in the medium term. A Stackelberg game approach is used to represent the hierarchical decision making process between the transit authority and opportunistic passengers. The heterogeneity of opportunistic passengers’ decisions to evade fare payment is taken into account. Numerical experiments show that a joint strategy-schedule approach provides good-quality unpredictable patrolling schedules with respect to the optimality gap for large-scale networks.