SOME BOUNDS FOR QUEUES

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Advanced Queuing Theory Analysis Probability and Statistical Research Age of Information Optimization

Abstract

SOME BOUNDS FOR QUEUES MASAO MORI Tokyo Institute of Technology (Received April 30; Revised August 5, 1974) We will give some bounds for variance of waiting time of system GI/G/l, which will give fairly good evaluations and are handy to calculate. And some bounds on mean waiting time and on probability of no wait will be improved for systems GI/G/l and GI/G/k. A notion of the virtual waiting time vector is useful! to derive some of these bounds.

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References

1963Introduction to the Theory of Queues.1955On the theory of queues with many servers 1970Inequalities in the Theory of Queues 1962Some Inequalities for the Queue GI/G/1 1970On the Optimality of Single-Server Queuing Systems 1972A low traffic approximation for queues

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1980Stochastic inequalities between customer-stationary and time-stationary characteristics of queueing systems with point processes 1977Further Stochastic Order Relations among GI/GI/1 Queues with a Common Traffic Intensity 1984Inequalities between Arrival Averages and Time Averages in Stochastic Processes Arising from Queueing Theory 1983Stationary queuing systems with dependencies 1983BOUNDS AND AN APPROXIMATION FOR SINGLE SERVER QUEUES

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