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Rates of convergence for queues in heavy traffic. I
Douglas P. Kennedy
Journal:

Advances in Applied Probability / Volume 4 / Issue 2 / August 1972

Published online by Cambridge University Press:

01 July 2016, pp. 357-381

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August 1972
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Estimates are given for the rates of convergence in functional central limit theorems for quantities of interest in the GI/G/1 queue and a general multiple channel system. The traffic intensity is fixed ≧ 1. The method employed involves expressing the underlying stochastic processes in terms of Brownian motion using the Skorokhod representation theorem.

Rates of convergence for queues in heavy traffic. II: Sequences of queueing systems
Douglas P. Kennedy
Journal:

Advances in Applied Probability / Volume 4 / Issue 2 / August 1972

Published online by Cambridge University Press:

01 July 2016, pp. 382-391

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August 1972
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Estimates are given for the rates of convergence in functional central limit theorems for the queue length process in a sequence of general multiple channel queues. The situation is considered where the traffic intensity in the nth. queue, ρn, tends to ρ ≧ 1 as n approaches infinity. This extends previous work by the author, [6], in which the traffic intensity was fixed ≧ 1.

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2 results

Rates of convergence for queues in heavy traffic. I

Rates of convergence for queues in heavy traffic. II: Sequences of queueing systems