A $$2~{\times }~2$$ 2 × 2 random switching model and its dual risk model

Anita Behme () and Philipp Lukas Strietzel ()
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Anita Behme: Technische Universität Dresden
Philipp Lukas Strietzel: Technische Universität Dresden

Queueing Systems: Theory and Applications, 2021, vol. 99, issue 1, No 2, 27-64

Abstract: Abstract In this article, a special case of two coupled M/G/1-queues is considered, where two servers are exposed to two types of jobs that are distributed among the servers via a random switch. In this model, the asymptotic behavior of the workload buffer exceedance probabilities for the two single servers/both servers together/one (unspecified) server is determined. Hereby, one has to distinguish between jobs that are either heavy-tailed or light-tailed. The results are derived via the dual risk model of the studied coupled M/G/1-queues for which the asymptotic behavior of different ruin probabilities is determined.

Keywords: Bipartite network; Bivariate compound Poisson process; Hitting probability; Coupled M/G/1-queues; Random switch; Regular variation; Ruin theory; Queueing theory; 60K25; 94C11 (primary); 60G10; 91G05 (secondary) (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11134-021-09697-9

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