Analysis of a clearing queueing system with setup times^∗

Department of Basic Courses, Shandong Women’s University, Jinan 250002, P.R. China
maqinghanzi@163.com

Received: 28 August 2013
Accepted: 27 May 2014

Abstract

We consider a Markovian clearing queueing system with setup times. When the system is empty, the server gets into the state of vacation. Once a new customer arrives the system, an exponential setup time is required before the server renders the service again. The customers are accumulated according to Poisson arrival process and the service times are exponentially distributed. Upon their arrivals, customers decide whether to join or balk the queue based on a natural linear reward-cost structure which reflects their desire for service and their unwillingness to wait. According to the state of server under some condition, we obtain the balking strategies of customers, the stationary distribution of system state, the expected queue length and the social optimal benefit. Finally, some numerical experiments describe how the expected queue length and the social optimal benefit depend on the arrival rate, the service time and the setup time.