Analysis of Semi-Open Queueing Network with Customer Retrials

서지정보

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· 저자명 : 김제숭, Sergey Dudin

초록

A semi-open queueing network is considered. The network of an arbitrary topology consists of a finite number ofnodes operation of which is modeled by single-server queueing systems with a buffer and an exponential service timedistribution. Customers arrive at the network according to a Markovian arrival process. The total number ofcustomers, which can be processed simultaneously, is restricted by a fixed in advance threshold. If the number ofcustomers in the network at a new customer arrival moment is less than the threshold, this customer is admitted forservice. Otherwise, the customer temporarily leaves the system (it is said that the customer joins the orbit) and retriesto get access to the network after the random time intervals duration of which has an exponential distribution. Thecapacity of the orbit is infinite. After the admission to the network, the customer starts sequential service in a randomnumber of nodes. The choice of the first and the subsequent nodes for service is made stochastically according to afixed stochastic vector and a transition probability matrix. The behavior of the network is described by thecontinuous-time Markov chain that belongs to the class of asymptotically quasi-Toeplitz Markov chains. This allowsto derive a transparent condition for the ergodicity of the chain and compute its steady-state distribution. Expressionsfor computation of various performance measures of the network are derived. Numerical results are presented. Themodel can be applied, e.g., for analysis and optimization of the operation of logistics and manufacturing systems,and the wireless telecommunication networks. To the best of our knowledge, queueing networks with correlatedarrival flows and retrials are not considered in the existing literature.*

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