M/C2 /1 Vacation Queue with Exceptional First Service and Server Breakdowns

Abstract

We have considered a single server multiple vacation queue with poisson input having different arrival rates for vacation, service and breakdown state of server. First service of each busy period is exceptional. Service time distribution is of coxian-2 type and subject to breakdown while in operation. The repair times, times to break down and length of vacation follow exponential distributions. In many fields like manufacturing. digital communication, bank services, health services, services are provided in two phases, where first phase is compulsory and second is optional. Using generating function technique mean queue length and average number of customers in the system are obtained. Numerical illustrations are also provided using graphs and tables.