A vacation queuing model with service breakdowns

摘要

In this paper we analyze a multiple-vacation queuing model, where he service station is subject to breakdown while operation. Service resumes immediately after a repair process, and a vacation starts at the end of each busy period. Arrivals follow a Poisson process with rates depending upon the system state, namely, vacation, service, or breakdown state. The repair times, times to breakdown following a repair or vacation, uninterrupted service times, and length of each vacation follow exponential distributions. Some results are also obtained when vacation, service, and repair times follow phase-type distributions.