Stationary cycles in a deterministic service system

Abstract

The article describes a deterministic service system, which receives requests from three queues. Characteristics of the service system such as intensity and rate of service request are stable and do not depend on time. The paper introduces definitions of the stationary mode and the cycle of service for requirements from queues. The main aim this article is to find necessary and sufficient conditions imposed on the duration of the service cycles, under which the existence of a stationary mode of operation of the service system is obtained and guaranteed. When a stationary service mode is implemented, the possibility of infinite accumulation of requests is excluded, while the order of servicing queues is set in advance and does not change in the future. Within the framework of the mathematical model of the deterministic service system, some technological limitations have been introduced. The fulfillment of these limitations is necessary for the construction of an adequate model. In particular, it is assumed that the service of the requirement can’t be interrupted. The proof of the main result of the item is based on the solution of inequalities obtained by considering the mathematical model of the functioning of the service system. In the proof was given a geometric interpretation of the set of admissible (providing a stationary mode) durations of continuous service for requests received from the queues. Refs 12. Figs 2.