Service in a Loop System

Alan G. Konheim · Bernd Werner Meister

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Advanced Queuing Theory Analysis Optimization and Search Problems Age of Information Optimization

Abstract

The statistical behavior of a loop service system is studied.The system consists of a main station, a server and N stations arranged on a loop.Customers arrive at each station according to a random process.The server makes successive tours along the loop bringing customers from the N stations to the main station.Two related measures of the grade of service are considered: the average queue length and the average virtual waiting time at each station.

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1961A Proof for the Queuing Formula: L = λ W 1952The theory of queues with a single server 1954On Queueing Processes with Bulk Service

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1979Message Delays in FDMA and TDMA Communication Channels 1984A golden ratio control policy for a multiple-access channel 1980The Analysis of a Statistical Multiplexer with Nonindependent Arrivals and Errors 1992Message delay analysis for TDMA schemes using contiguous-slot assignments 1976Buffer Behavior with Poisson Arrivals and Bulk Geometric Service 1979Buffer Behavior in Computer Communication Systems 1991Message delay and queue-size analysis for circuit-switched TDMA systems 1985Performance analysis of token ring local area networks

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