Reference for citation: Peschansky А. I. Stationary characteristics of GI/G/1/1 queuing system in terms of the renewal process. Journal of Instrument Engineering. 2023. Vol. 66, N 5. P. 373—388 (in Russian). DOI: 10.17586/0021-3454-2023-66-5-373-388.

Abstract. The semi-Markov process describing queuing system operation is analyzed as a renewal. Its regeneration points are the moments of requests arrivals to the free system. Formulas are established for calculating the following characteristics of the system for a regeneration cycle: average numbers of incoming, serviced and lost requests; average residence time of the system in the free state; average total sojourn times in the system for one and two claims. The final probabilities of the system physical states, average stationary sojourn times in the states, in the queue and in the system are expressed in terms of the renewal process characteristics.

Keywords: single-server queuing system with one queue place, renewal process, the number of arrivals, of complete and lost requests per renewal cycle, total sojourn times in states, stationary characteristics of the system

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