A queueing system for performance evaluation of a Markovian supercomputer model

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.