Strategic reneging in service systems with working breakdowns

Queueing Systems, vol. 110

Abstract

Abstract In this study, we analyze the reneging behavior of customers in a Markovian M/M/1 queue with an alternating service process, representing a normal operation mode and a working repair mode with reduced service speed. The customers are strategic and, as they continuously observe the system’s state, they decide whether to stay or to renege. For this model, we derive equilibrium customer reneging strategies and the corresponding performance measures of the system, considering both the baseline model with discrete units of customers and its fluid counterpart. To capture the effect of reneging, we compare their performance with similar systems, operating under a no-reneging policy. Both theoretical findings, as well as numerical experiments, reveal that allowing reneging significantly affects system performance. Finally, to assess the quality of the fluid approximation we conduct a numerical comparison between the fluid and the baseline version of the model.

Authors 3

1. Odysseas Kanavetas corresponding Aachen Mathematical Institute

   Leiden University

   Affiliation as printed

   Mathematical Institute, Leiden University, Niels Bohrweg, 2333 CA, Leiden, The Netherlands

2. Dimitrios Logothetis Aachen Mathematical Institute

   Leiden University

   Affiliation as printed

   Mathematical Institute, Leiden University, Niels Bohrweg, 2333 CA, Leiden, The Netherlands

3. Athanasia Manou

   National and Kapodistrian University of Athens

   Affiliation as printed

   Department of Mathematics, National and Kapodistrian University of Athens, Panepistemiopolis, 15784, Athens, Greece