Waiting Lines and Times in a System with Polling

Alan G. Konheim · Bernd Werner Meister

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Advanced Queuing Theory Analysis Network Traffic and Congestion Control Age of Information Optimization

Abstract

A communication system consisting of a number of buffered input terminals connected to a computer by a single channel is analyzed. The terminals are polled in sequence and the data is removed from the terminal's buffer. When the buffer has been emptied, the channel, for an interval of randomly determined length, is used for system overhead and/or to transmit data to the terminals. The system then continues with a poll of the next terminal. The stationary distributions of the length of the waiting line and the queueing delay are calculated for the case of identically distributed input processes.

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1987On the Optimal Control of Two Queues with Server Setup Times and Its Analysis 1988The Analysis of Random Polling Systems 1985Symmetric queues served in cyclic order 1988Waiting times in discrete-time cyclic-service systems 1989Dynamic priority rules for cyclic-type queues 1985Mean message waiting times in symmetric multi-queue systems with cyclic service 1986Average Delay Approximation of M/G/1 Cyclic Service Queues with Bernoulli Schedules 1992Cyclic reservation schemes for efficient operation of multiple-queue single-server systems

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