Closed Gordon – Newell network with single-line poles and exponentially limited request waiting time

Abstract

Objectives. An exponential queuing network with single-line poles is considered, which differs from the Gordon – Newell network only that the waiting time for service requests at the poles of the network is a random variable with conditional distribution for a fixed number of requests at the pole as an exponential distribution. Requests at poles and requests that did not get the service are moving through the network in accordance with different routing matrices. The objective was to investigate a queuing system and to establish sufficient conditions for its ergodicity, also to find stationary distribution of given network.Methods. Methods of mathematical modeling and analytical research of queuing networks are used.Results. A theorem generalizing the Gordon – Newell theorem is proved.Conclusion. The possibility of varying the routing matrices of served and unserved requests makes it possible to take into account a wide variety of practical situations and reduce the load in the bottlenecks of the network under study. It is very important in the design and modernization of information and computer networks.