Development of Approximate Calculation Methods for Multiserver Priority Systems

Abstract

The article addresses the pressing issue of enhancing the efficiency and reliability of multiserver queuing systems (QS) with absolute priorities. Such QS are critically important components in the management of complex real-time technical complexes, where requirements for performance and task resolution speed are extremely high. It is established that traditional exact analytical methods, which are effective for single-server systems, become impractical for the multiserver case due to the exponential growth of the state space, especially when it is necessary to account for queue lengths and the diversity of requests. To overcome these limitations, a combined approach is proposed, based on integrating approximate analytical calculations with the results of large-scale simulation modeling. Simulation experiments performed a threefold function: providing initial data, generating and verifying hypotheses, and conducting the final comprehensive system check. As a result of the research, engineering techniques were developed and substantiated for estimating three key system characteristics. Firstly, the average waiting time was approximated using the two-moment complementary Weibull distribution function. Secondly, a generalized formula for the continuous busy period 𝜋(𝑛) was derived, incorporating a novel correction factor Δ. This factor accounts simultaneously for the impact of channel utilization 𝜌, the service coefficient of variation 𝑣, and the number of channels 𝑛. Thirdly, an approximate formula for calculating the expected number of interruptions 𝑘! ) for a request of a specific priority was developed. The validity of the developed formulas was systematically verified by comparing calculated and simulated data obtained from 200 000 observations. The high consistency of the results confirms that the proposed methodology is a reliable, simple, and practically oriented tool for the effective design and optimization of multiserver priority QS, particularly in scenarios where rigorous mathematical analysis is infeasible.