Relationships between characteristics in periodic Poisson queues
type: Item
instance of: scholarly article
title: Relationships between characteristics in periodic Poisson queues
zbMATH Open document ID: 0676.60087
DOI: 10.1007/BF01150853
author: Tomasz Rolski
published in: Queueing Systems
publication date: 1989-01-01T00:00:00Z
review text: For the single server queue with periodic Poisson input and iid service times \(S_ i\), the workload, \(V^ p(t)\), the number of customers present, \(L^ p(t)\), and the departure rate, \(u^ p(t)\), are studied. Day equilibrium is assumed, i.e. it is assumed, that \(V^ p(t)\sim V^ p(t+p)\), where p is the period of the input. Results are: (i) E [V\({}^ p(t)]<\infty\) provided E [S\({}^ 2_ i]<\infty;\) (ii) E [S\({}_ i] E [L^ p(t)]=(\leq)(\geq)E [V^ p(t)]\), provided that \(S_ i\) is exponentially (NBUE), (NWUE) distributed; (iii) \(u^ p(t)=a(t)-(d/dt)E [L^ p(t)]\), where a(t) denotes the arrival intensity function.
Mathematics Subject Classification ID: 60K25
zbMATH DE Number: 4107893
zbMATH Keywords: output processes
zbMATH Keywords: workload
zbMATH Keywords: queue length
zbMATH Keywords: periodic Poisson input
zbMATH Keywords: arrival intensity function
reviewed by: R. Schaßberger
MaRDI profile type: Publication
cites work: Q3909796
cites work: Doubly stochastic Poisson processes
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cites work: On queues with periodic Poisson input
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description: scientific article; zbMATH DE number 4107893