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Title: Performance analysis of a queuing system with vacation and correlated train arrivals
Authors: Kamoun, F. 
Issue Date: 2007
Journal: International Conference on High Performance Computing, Networking and Communication Systems 2007, HPCNCS 2007 
Conference: 2007 International Conference on High Performance Computing, Networking and Communication Systems, HPCNCS 2007; Orlando, FL; United States; 9 July 2007 through 12 July 2007; Code 96743 
Abstract: In this paper, we consider a discrete-time queue with a correlated train arrival process and a single server subjected to random vacation (server interruptions). We model the server vacation by a correlated Markovian on/off process with geometrically distributed on and off periods. We derive an expression for the functional equation describing the transient evolution of this queuing system. This functional equation is then manipulated and transformed into a mathematical tractable form. This allows us to derive the probability generating function of the buffer occupancy. From this pgf, closed-form expressions for various performance measures, such as mean and variance of queue length and customer delay can be derived. Finally, we illustrate our solution technique with some numerical examples, whereby we demonstrate the negative effect of correlation in the vacation process on the performance of the queue. The paper presents new insights into the performance analysis of discrete-time queues with correlated arrivals and service interruption and it also covers some previously published results as a special case.
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