Stationary queues with one autonomous server
type: Item
instance of: scholarly article
title: Stationary queues with one autonomous server
zbMATH Open document ID: 0567.60087
DOI: 10.1016/0304-4149(85)90027-4
published in: Stochastic Processes and their Applications
publication date: 1985-01-01T00:00:00Z
review text: Given a stationary stochastic continuous demand of service \(\sigma (\theta_ t\omega)dt\) with \(\int \sigma (\omega)P(d\omega)<1\), the author constructs a real stationary point process \((T_ n, n\in Z)\), \(T_ n<T_{n+1}\), \(\lim_{n\to \pm \infty}T_ n=\pm \infty\), such that \(T_{n+1}-T_ n=D+\int^{T_ n}_{T_{n-1}}\sigma \theta_ t dt\), for a given constant \(D>0.\) These point processes correspond to a service discipline for which a single server services during the time \([T_ n,T_{n+1})\) the demand of service accumulated during the preceding interval \([T_{n-1},T_ n)\) and takes a rest of fixed duration D.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B22
Mathematics Subject Classification ID: 60G55
zbMATH DE Number: 3905606
zbMATH Keywords: stationary stochastic continuous demand of service
zbMATH Keywords: single server
author: Jacques Neveu
reviewed by: D. P. Kennedy
MaRDI profile type: Publication
full work available at URL: 0304-4149(85)90027-4
OpenAlex ID: W1969997028
cites work: Q4082108
cites work: Q3955608
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description: scientific article; zbMATH DE number 3905606