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

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