Rates of convergence for queues in heavy traffic. I

Douglas P. Kennedy

18 citations0/0 files storedAdvances in Applied Probability

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Advanced Queuing Theory Analysis Stochastic processes and statistical mechanics Probability and Risk Models

Abstract

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.

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1970Multiple channel queues in heavy traffic. I 1970Multiple channel queues in heavy traffic. II: sequences, networks, and batches 1971Multiple channel queues in heavy traffic 1964Some Limit Theorems in the Theory of Mass Service 1965Some Limit Theorems in the Theory of Mass Service, II Multiple Channels Systems 1971Weak convergence theorems for priority queues: preemptive-resume discipline 1971Weak convergence theorems for priority queues: preemptive-resume discipline 1970Multiple channel queues in heavy traffic. III: random server selection

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1990Strong approximations for multiple channel queues in heavy traffic 1972Complements to heavy traffic limit theorems for the GI/G/1 queue 1977The stable M / G /1 queue in heavy traffic and its covariance function

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