A zero-or-one law in aggregated closed queueing networks
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For a closed queueing network with single-server nodes, we prove that if the total number of requests, the number of servers in one of the nodes, and service rates in all other nodes are made n times as large, then the stationary number of requests in the multiserver node divided by n converges in probability as n → ∞ to a positive constant, determined by parameters of the original network, with geometric convergence rate. Single-server nodes in the constructed network can be interpreted as repair nodes, the multiserver node as a set of workplaces, and requests as elements in a redundancy-with-repair model.
KeywordsInformation Transmission Service Rate Transportation Problem Queueing System Original Network
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