Sharma, Vinod (1993) Open queueing networks in discrete time- some limit theorems. In: Queueing Systems, 14 (1-2). pp. 159-175.
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A finite number of nodes, each with a single server and infinite buffers, is considered in discrete time. The service may be FIFO and the service times are constant. The external arrivals and the routing decision variables form a general stationary sequence. Stability of the system is proved under these assumptions. Extension to multiple servers at a node and general stationary distributions holds. If the external input is i.i.d. and the routing is Markovian then stochastic ordering, continuity of stationary distributions, rates of convergence, a functional CLT and a functional LIL and various other limit theorems for the queue length process are also proved. Generalizations to multiple servers at nodes, customers with priority, multiple customer classes, general service length and Markov modulated external arrival cases are discussed.
|Item Type:||Journal Article|
|Additional Information:||Copyright of this article belongs to Springer.|
|Keywords:||Queueing networks;Nonproduct form networks;Stability;Stochastic continuity;Functional limit theorems|
|Department/Centre:||Division of Electrical Sciences > Electrical Engineering|
|Date Deposited:||07 Jul 2006|
|Last Modified:||19 Sep 2010 04:29|
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