재시도 준개방형 대기행렬네트워크 분석

Abstract

A semi-open queueing network is considered. The network of an arbitrary topology consists of a finite number of nodes operation of which is modeled by single-server queueing systems with a buffer and an exponential service time distribution. Customers arrive at the network according to a Markovian arrival process. The total number of customers, which can be processed simultaneously, is restricted by a fixed in advance threshold. If the number of customers in the network at a new customer arrival moment is less than the threshold, this customer is admitted for service. Otherwise, the customer temporarily leaves the system (it is said that the customer joins the orbit) and retries to get access to the network after the random time intervals duration of which has an exponential distribution. The capacity of the orbit is infinite. After the admission to the network, the customer starts sequential service in a random number of nodes. The choice of the first and the subsequent nodes for service is made stochastically according to a fixed stochastic vector and a transition probability matrix. The behavior of the network is described by the continuous-time Markov chain that belongs to the class of asymptotically quasi-Toeplitz Markov chains. This allows to derive a transparent condition for the ergodicity of the chain and compute its steady-state distribution. Expressions for computation of various performance measures of the network are derived. Numerical results are presented. The model can be applied, e.g., for analysis and optimization of the operation of logistics and manufacturing systems, and the wireless telecommunication networks.