СРЕДНЯЯ ДЛИНА ОЧЕРЕДИ ДЛЯ СИСТЕМ МАССОВОГО ОБСЛУЖИВАНИЯ С КОРРЕЛИРОВАННЫМИ ВХОДНЫМИ ПОТОКАМИ

Abstract

In multiservice packet-switched networks, the packet flow differs significantly from the Poisson flow, since these flows are generated by many sources of requests for services that are significantly different from each other. All this leads to the fact that the flows in multiservice networks are characterized by uneven arrival of requests and packets. Packages are grouped into "bundles" at some time intervals and are practically absent at other intervals. The random process of claims (packets) entering the system is characterized by a distribution law that establishes a relationship between the values ??of a random variable and the probabilities of occurrence of the indicated values. In most cases, such a flow is characterized by a distribution function of time intervals between neighboring claims, and the process of their processing is characterized by a probability distribution function of service time intervals. The mathematical model of the simplest single-channel queuing systems (QS) in case of incoming flow with arbitrary correlation. For this QS, various generalizations of the Khinchin-Pollachek formula of the average queue length. An interval model of the incoming flow is proposed, within which an expression of the average queue length through unconditional moments is obtained second order. All results were obtained with very general assumptions of ergodicity and stationarity. Are given results of numerical experiments confirming theoretical conclusions.