Relationships and decomposition in the delayed Bernoulli feedback queueing system

Relationships and decomposition in the delayed Bernoulli feedback queueing system

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Article ID: iaor1988777
Country: Israel
Volume: 25
Issue: 1
Start Page Number: 169
End Page Number: 183
Publication Date: Mar 1988
Journal: Journal of Applied Probability
Authors: ,
Abstract:

For the delayed Bernoulli feedback queue with first come-first served discipline under weak assumptions a relationship for the generating functions of the joint queue-length distribution at various points in time is given. A decomposition for the generating function of the stationary total queue length distribution has been proven. The Laplace-Stieltjes transform of the stationary joint workload distribution function is represented by its marginal distributions. The arrival process is Poisson, renewal or arbitrary stationary, respectively. The service times can form an i.i.d. sequence at each queue. Different kinds of product form of the generating function of the joint queue-length distribution are discussed.

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