Transient and Stationary Distributions for the GI/G/k Queue with Lebesgue-Dominated Inter-Arrival Time Distribution |
| |
Authors: | Breuer Lothar |
| |
Affiliation: | (1) FB IV – Informatik, Universität Trier, 54286 Trier, Germany |
| |
Abstract: | In this paper, the multi-server queue with general service time distribution and Lebesgue-dominated iid inter-arival times is analyzed. This is done by introducing auxiliary variables for the remaining service times and then examining the embedded Markov chain at arrival instants. The concept of piecewise-deterministic Markov processes is applied to model the inter-arrival behaviour. It turns out that the transition probability kernel of the embedded Markov chain at arrival instants has the form of a lower Hessenberg matrix and hence admits an operator–geometric stationary distribution. Thus it is shown that matrix–analytical methods can be extended to provide a modeling tool even for the general multi-server queue. |
| |
Keywords: | GI/G/k multi-server queue discrete time |
本文献已被 SpringerLink 等数据库收录! |