Social optimization in M/M/1 queue with working vacation and N-policy

¹ School of Economics and Management, Shanxi University, Taiyuan 030006, China
² Institute of Management and Decision, Shanxi University, Taiyuan 030006, China
³ School of Mathematics and Statistics, Carleton University, Ottawa K1V5B6, Canada
⁴ Faculty of Finance and Banking, Shanxi University of Finance and Economics, Taiyuan 030006, China

^* Corresponding author: e-mail: maqq0814@sina.com

Received: 29 December 2015
Accepted: 17 May 2017

Abstract

This paper deals with the N-policy M/M/1 queueing system with working vacations. Once the system becomes empty, the server begins a working vacation and works at a lower service rate. The server resumes regular service when there are N or more customers in the system. By solving the balance equations, the stationary probability distribution and the mean queue length under observable and unobservable cases are obtained. Based on the reward-cost structure and the theory of Markov process, the social welfare function is constructed. Finally, the impact of several parameters and information levels on the mean queue length and social welfare is illustrated via numerical examples, comparison work shows that queues with working vacations(WV) and N-policy have advantage in controlling the queue length and improving the social welfare.