Average number of clients in the queuing systems with limited average time

Abstract

Queuing systems with some kind of constraint on the system's control parameters have always been of particular interest in queuing theory. The point in this case is that systems with various constraints are frequently in demand when a variety of applied problems in different, sometimes very far from each other subject areas, are solved. In particular, logistics traditionally connected with the theory of mass service, as well as such innovative areas of modern applications as, for example, teletraffic theory, telecommunication theory, and many others can be referred to such subject areas. A mathematical model of an open multi-channel queuing system with a limited average residence time for claims in a queue containing “impatient” and “patient claims” is presented. With the help of the Kummer confluent hypergeometric function, a detailed mathematical formalization of the model was carried out and the basic probability characteristics of queuing systems of this type were computed.