An algorithmic analysis of multi-server vacation model with service interruptions

Motivated by the trade-off between reliability and utilization level of a stochastic service system, we considers a Markovian multi-server vacation queueing system with c unreliable servers. In such a system, some servers may not be available due to either planned stoppage (vacations) or unplanned service interruptions (server failures). The vacations are controlled by a threshold policy. With this policy, at a service completion instant, if d (⩽c) servers become idle, they take a vacation together and will keep taking vacations until they find at least c − d + 1 customers are in the system at a vacation completion instant, and then they return to serve the queue. In addition, all on-duty servers are subject to failures and can be repaired within a random period of time. We formulate a quasi-birth–death (QBD) process, establish the stability condition, and develop a computational algorithm to obtain the stationary performance measures of the system. Numerical examples are presented to show the performance evaluation and optimization of such a system. The insights gained from this model help practitioners make capacity and operating decisions for this type of waiting line systems.

► We model a multi-server queueing system with server interruptions and vacations.
► While server vacations represent planned server’s doing other jobs, server interruptions represent unplanned server failures.
► We examine the effects on the system performance of server vacations and interruptions.
► System performance depends on the server’s reliability and the repair speed.