The theory of networks of single server queues and the tandem queue model

[摘要] We consider the stochastic behavior of networks of single server queues when successive service times of a given customer are highly correlated. The study is conducted in two particular cases: 1) networks in heavy traffic, and 2) networks in which all successive service times have the same value (for a given customer), in orderto avoid the possibility of breaking up the busy periods. We then show how thelocal queueing delay(for an arbitrary customer) can be derived through anequivalent tandem queueon the condition that one other local queueing delay is added: the jitter delay due to the independence of partial traffic streams.We consider a practical application of the results by investigating the influence of long packets on the queueing delay of short packets in modern packet switched telecommunication networks. We compare these results with the results given by traffic simulation methods to conclude that there is good agreement between results of calculation and of traffic simulation.

[学科分类] 应用数学