STATIONARY CHARACTERISTICS OF AN UNLIMITED QUEUE SINGLE-CHANNEL SYSTEM WITH REGARD TO SERVICE QUALITY CONTROL
Annotation
A service system is studied, in which, upon completion of servicing of each application, instant control of the quality of its service is carried out. In case of unsatisfactory quality, the application is sent for repeated services, which are carried out until the quality is considered satisfactory. A semi-Markov process of system functioning is constructed, and the stationary distribution of the embedded Markov chain is found. Analogues of the Pollaczek — Khinchin formula for generating functions of the stationary probabilities are obtained. The system stationary characteristics depending on the probability of quality service are determined: the stationary distribution of the queue over time, the average stationary duration of stay in a state, the average number of requests in the queue and system, the average duration of the request stay in the queue and system.
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