A multi-server queueing model with retrial connection arrivals as a model for optimisation of the traffic control
چکیده
To cite this article: CheSoong Kim & Sergey Dudin (2012): A multi-server queueing model with retrial connection arrivals as a model for optimisation of the This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. We consider a multi-server queueing model with a finite buffer and requests arriving in connections. The number of requests in a connection is random and unknown at the connection initiation instant. Requests, which belong to the connection, arrive in accordance with a Poisson process. Admission of connections to the system is regulated by means of so-called tokens. The pool of tokens is finite. If a connection arrives and there are no tokens available, it leaves the system forever or joins the orbit and retries for access later on. The steady-state distribution of the system is analysed. The problem of the throughput maximisation under the constraint that the request loss probability does not exceed a predefined value is numerically solved. The effect of the retrial intensity, correlation and variation in the arrival process and the probability to leave the system if tokens are not available is numerically highlighted. 1. Introduction Queueing systems are successfully applied for performance evaluation, capacity planning and optimisation of many real world objects and processes. Many queueing systems have a finite capacity. So, some arriving requests can be lost. If no priorities are assumed and the arrival flow is ordinary, the standard admission discipline is very simple: only the requests, which arrive when the system is full, are rejected. If the requests can arrive in batches, the admission discipline is a bit more complicated. It is necessary to take into account whether (i) the requests of a batch are independent of each other and the loss of some requests does not affect other requests or (ii) the requests of a …