This article is cited in 2 papers

A queueing system for performance evaluation of a Markovian supercomputer model

R. V. Razumchik^a, A. S. Rumyantsev^b, R. M. Garimella<sup>c

a</sup> Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
^b Institute of Applied Mathematical Research of the Karelian Research Center of the Russian Academy of Sciences, 11 Pushkinskaya Str., Petrozavodsk 185910, Russian Federation
^c Mahindra University, 62/1A Bahadurpally Jeedimetla, Hyderabad 500043, India

Abstract: Consideration is given to the well-known supercomputer model in the form of a Markovian nonwork-conserving two-server queueing system with unlimited queue capacity, in which customers are served by a random number of servers simultaneously. For the first time, it is shown that its basic probabilistic characteristics can be calculated from an unrelated single-server queueing system with infinite capacity, work conserving scheduling, and forced customers' losses. Based on the known matrix-analytic techniques for quasi-birth-and-death processes, it is shown that in certain special cases, the transient queue-size distribution can be found (in terms of Laplace transform) using the Level Crossing Information method and has a matrix-geometric form. Numerical examples which illustrate some properties of the established connection between the two queueing systems are provided.

Keywords: supercomputer model, queueing system, nonwork-conserving scheduling, transient regime.

Received: 15.04.2023

DOI: 10.14357/19922264230209