On strategic customers in the group-merging Israeli queue

This paper introduces the Group-Merging Israeli Queue, an extension of the Israeli Queue model, where arriving customers, in addition to joining or creating groups, can merge two adjacent waiting customers and their respective groups into a single group for batch service. The Group-Merging Israeli Queue is formulated, and various performance measures are calculated. Furthermore, strategic customer behavior in the system is analyzed. Novel findings include the derivation of customer joining thresholds under various scenarios and the demonstration of the effect of the system parameters on customer behavior. Despite customer strategic behavior, the study reveals that the queue can remain unbounded. In addition, an economic study from the system’s perspective is presented, from which managerial decisions are derived.