Stochastic Bounds for Fast Jackson Networks
نویسنده
چکیده
We consider a Jackson-type network, each of whose nodes contains N identical channels with a single server. Upon arriving at a node, a task selects m of the channels at random, and enters the one with the shortest queue. We provide stochastic bounds for the distribution of the state of the network in terms of the behaviour of independent nodes of the same type. The bounds are asymptotically tight when every node is at least fully loaded. This is a generalisation of a result of W.A. Massey giving bounds for the behaviour of a standard Jackson network in terms of that of independent M=M=1 queues.
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