Imbedded and non-imbedded stationary characteristics of queueing systems with varying service rate and point processes

Dieter König · Volker Schmidt

42 citations0/0 files storedJournal of Applied Probability

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Advanced Queuing Theory Analysis Probability and Statistical Research Stochastic processes and statistical mechanics

Abstract

In this paper a unified approach is used for proving relationships between customer-stationary and time-stationary characteristics of service systems with varying service rate and point processes. This approach is based on an intensity conservation principle for general stationary continuous-time processes with imbedded stationary marked point processes. It enables us to work under weaker independence assumptions than usual in queueing theory.

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References

1963Introduction to the Theory of Queues.1983The Single Server Queue 1976Stochastic Processes in Queueing Theory 1976On Regenerative Processes in Queueing Theory 1977Level Crossings in Point Processes Applied to Queues: Single-Server Case 1977On up- and downcrossings 1979A formal approach to queueing processes in the steady state and their applications 1963THE LIMITING DISTRIBUTION OF THE VIRTUAL WAITING TIME AND THE QUEUE SIZE FOR A SINGLE-SERVER QUEUE WITH RECURRENT INPUT AND GENERAL SERVICE TIMES

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1984Stationary queue-length and waiting-time distributions in single-server feedback queues 1989EPSTA: The coincidence of time-stationary and customer-stationary distributions 1980Stochastic inequalities between customer-stationary and time-stationary characteristics of queueing systems with point processes 1983On the identification of Poisson arrivals in queues with coinciding time-stationary and customer-stationary state distributions 1989On stability of state-dependent queues and acyclic queueing networks

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