Unreliable service system with strategic customers: effect of abandonments and repair time

In this study, we analyze the reneging behavior of strategic customers in a Markovian queueing system with a single server which is subject to breakdowns. In the event of a breakdown, the server is replaced with a secondary backup unit which serves at a diminished service speed. The restoration of the primary unit is possible only when the system is empty and through a repair process. Reneging is possible and the customers may decide to abandon the system at any time. To focus on the effect of reneging, we also consider the case where reneging is prohibited and the customers decide exclusively, whether to join or balk. We also consider the case where the repair duration is instantaneous. For these models, we derive the equilibrium strategies for the customers and evaluate the performance of the system under both scenarios. Moreover, we discuss the effects of the server repairing procedure and present numerical experiments that reveal key differences in the customer strategic behavior. We identify cases where reneging is beneficial in terms of social welfare, as well as cases where prohibiting reneging ensures greater welfare.