A vacation queueing model with first exceptional service, encouraged arrivals and server breakdowns

Abstract

This paper examines a single server queueing model with multiple vacations, encouraged customer arrivals and operational breakdowns. Service resumes after repairs with handling first customer of every busy period exceptionally. Additionally vacation is taken by server after each busy period. It takes another vacation if he finds no customer in the queue. Customers arrive according to poisson process with different rates during vacation, active service and repair process. Active arrival occurs in accordance with percentage change due to encouraged customers. For both type of customers (first and followed) uninterrupted service times, vacation times and repair times follow exponential distribution. Using probability generating function we found mean queue length and derived existence condition for steady state queue length. Numerical examples are also presented.