Batch Service Queueing System Associated with Inventory Transport

This paper considers a single server batch service queueing system in which service is provided in at most k stages. A batch of customers is admitted for service under GBS - rule (with minimum batch size a and maximum batch size b). The customers have the choice to leave the system after service completion from any stage. The service time of a customer in a stage depends on the stage as well as the number of customers being served in that stage. The stability of such a system is investigated and key performance measures computed based on system state distribution. The time required to provide service to a batch of specified size is analyzed. An optimization problem is considered and a numerical example provided.