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

Ma, Qing-Qing; Li, Ji-Hong; Liu, Wei-Qi

RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 2, pp. 439-452.

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.

Classification : 90B22, 60K25, 68M20
Mots clés : Markov process, working vacations, N-policy, social optimization

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