Investigation of preemptive RQ-system M| GI| 1 under extensive delay

Abstract

The relevance of work is caused by wide application of RQ-systems in everyday life. The main aim of the study is to investigate the preemptive RQ-system M | GI | 1, to find out joint distribution of probabilities of the demand number in a source of repeated calls and the device conditions. The methods used in the study: To achieve the aim the asymptotic analysis was used under extensive delay. The authors found the first asymptotics in which stationary distribution of the device condition probabilities was determined. The capacity of preemptive RQ-system of M | by GI | 1 was obtained as well. The authors found out a condition of existence of a stationary mode the second asymptotics where the asymptotic characteristic function of a number of demands in a source of repeated calls was shown. The results: The capacity S is found in the preemptive RQ-system of M | GI | 1 operation. Based on this fact the conclusions were drawn on stationary mode existence. The asymptotic characteristic function of a number of demands in a source of repeated calls was found out at final nonzero value S. It was shown that it is the characteristic function of a random variable distributed by a normal probability law.

Keywords

• RQ-system
• asymptotic analysis
• system loading
• capacity