We show that the end-to-end delay of the tagged flow in a tandem queueing network, and more generally in a tree network, is completely dominated by one of the queues. The dominant queue is the one with the maximal Hurst parameter. If several queues have the same maximal Hurst parameter, then we have to compare the ratio 1/s * (1- r)^H to determine the dominant queue, where r is the load of the queue.

In the case that the tagged flow is controlled through a window based congestion control mechanism, the end-to-end delay is still asymptotically Weibullian with the same shape parameter. We provide upper and lower bounds on the constant that determines the scale parameter of the corresponding Weibull distribution.

This is joint work with Marc LeLarge and Zhen Liu.

]]>Industrial and Systems Engineering

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