A \(2\times 2\) random switching model and its dual risk model. (English) Zbl 1483.90043
Summary: 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.
MSC:
| 90B22 | Queues and service in operations research |
| 60K30 | Applications of queueing theory (congestion, allocation, storage, traffic, etc.) |
| 60K10 | Applications of renewal theory (reliability, demand theory, etc.) |
Keywords:
bipartite network; bivariate compound Poisson process; hitting probability; coupled \(M/G/1\)-queues; random switch; regular variation; ruin theory; queueing theoryReferences:
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