Analysis of an M/M/1 queueing system with impatient customers and a variant of multiple vacation policy

Dequan Yue, Wuyi Yue, Zsolt Saffer, Xiaohong Chen
2013 Journal of Industrial and Management Optimization  
In this paper, we consider an M/M/1 queueing system with impatient customers and a variant of multiple vacation policy, where we examine the case that customer impatience is due to the servers' vacation. Whenever a system becomes empty, the server takes a vacation. However, the server is allowed to take a maximum number of vacations, denoted by K vacations, if the system remains empty after the end of a vacation. We derive the probability generating functions of the steady-state probabilities
more » ... ate probabilities and obtain the closed-form expressions of the system sizes when the server is in different states. In addition, we obtain the closed-form expressions for other important performance measures. Finally, we present some numerical results. Keywords Queue, a variant of multiple vacation, impatience, probability generating function, mean system size.
doi:10.3934/jimo.2014.10.89 fatcat:nsaxcts5zzfcrm67ah2ybyxoxi