06091250

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06091250 Xu, Zurun Zhu, Yijun Sun, Guiyong Li, Minjie The $Geo/Geo/1$ queue model with multiple vacations, negative customers, and the $\langle p,N\rangle$ policy set-up time. Chin. J. Eng. Math. 28, No. 6, 794-802 (2011). 2011 Editorial Board of Chinese Journal of Engineering Mathematics, Faculty of Science, Xi'an Jiaotong University, Xi'an ZH negative customers set-up time matrix-geometric approach conditional stochastic decomposition Summary: This paper considers a $Geo/Geo/1$ discrete time queueing model with multiple vacations, in which the $\langle p,N\rangle$ policy of the set-up time and negative customers are introduced. The start-up period is constrained by the $\langle p,N\rangle$ policy. When negative customers arrive, they need no service, but remove positive customers who are receiving service one by one. Using the quasi-birth-and-death process and the matrix-geometric approach, we first discuss the equilibrium conditions for the steady-state distribution of the queue length. And the concise expressions for the steady-state distribution of the queue length are derived. Furthermore, the conditional stochastic decomposition structure of the queue length under steady state and the distribution of the additional queue length caused by vacations are also obtained.