The M A P / P H / 1 / N queue with flows of customers as a model for traffic control in telecommunication networks

• Published in: Performance evaluation Vol. 66; no. 9; pp. 564 - 579
• Main Authors: Kim, Chesoong, Dudin, Sergey, Klimenok, Valentina
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.09.2009
• Subjects: Loss probability; Markovian arrival process; Matrix analytic methods; Performance modeling; Phase type service; Reactive admission control; Performance modeling; Markovian arrival process; Matrix analytic methods; Reactive admission control; Phase type service; Loss probability
• ISSN: 0166-5316; 1872-745X
• DOI: 10.1016/j.peva.2009.04.002

A single-server queueing model with finite buffer and flows of customers is considered. Flow means a group of customers which should be sequentially processed in the system. In contrast to the standard batch arrival when a whole group of customers arrives into the system at one epoch, we assume that the customers of an accepted flow arrive one by one in exponentially distributed times. Service time has Phase type ( P H ) distribution. Generation of flows is described by the Markov Arrival Process ( M A P ). A flow consists of a random number of customers. This number is geometrically distributed and is not known at a flow arrival epoch. The number of flows, which can be admitted into the system simultaneously, is subject to control. Accepted flow can be lost, with a given probability, in the case of any customer from this flow rejection. Analysis of the joint distribution of the number of flows and customers in the system, flow loss probability and sojourn time distribution is implemented by means of the matrix technique and method of catastrophes. The effect of control on the main performance measures of the system is demonstrated numerically. The influence of correlation in the arrival process of flows, variation of service time and probability of a flow loss in case of any customer from this flow rejection is illustrated.