Moments in Tandem Queues

Moments in Tandem Queues

We settle a conjecture concerning necessary conditions for finite mean steady-state customer delay at the second node of a tandem queue, using as an example a stable tandem queue with mutually independent i.i.d. interarrival and service times. We assume that the service times have infinite variance...

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Bibliographische Detailangaben
Veröffentlicht in:Operations Research. - Institute for Operations Research and the Management Sciences, 1956. - 46(1998), 3, Seite 378-380
1. Verfasser: Scheller-Wolf, Alan (VerfasserIn)
Weitere Verfasser: Sigman, Karl
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 1998
Zugriff auf das übergeordnete Werk:Operations Research
Schlagworte:Sample path properties Queuing theory: finite moments of steady-state distribution Applications: customer delay Stochastic Processes Mathematics Philosophy Business Applied sciences
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520 |a We settle a conjecture concerning necessary conditions for finite mean steady-state customer delay at the second node of a tandem queue, using as an example a stable tandem queue with mutually independent i.i.d. interarrival and service times. We assume that the service times have infinite variance at the first node, finite variance at the second node, and smaller mean at the first node than at the second node. We show that this causes infinite mean stationary delay at the second node. Thus, in general, when the mean service time is smaller at the first node than at the second, finite variance of service times at node 1 is necessary for finite mean delay at node 2. This confirms a conjecture made by Wolff. Our result complements sufficiency conditions previously published by Wolfson; together these necessary and sufficient conditions are presented as a theorem at the conclusion of the paper. Our proof uses a known duality between risk processes and queues. 
540 |a Copyright 1998 The Institute for Operations Research and the Management Sciences 
650 4 |a Sample path properties 
650 4 |a Queuing theory: finite moments of steady-state distribution 
650 4 |a Applications: customer delay 
650 4 |a Stochastic Processes 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Applied statistics  |x Descriptive statistics  |x Statistical distributions  |x Distribution functions  |x Probability distributions  |x Mathematical moments 
650 4 |a Philosophy  |x Logic  |x Metalogic  |x Logical truth  |x Sufficient conditions 
650 4 |a Business  |x Business economics  |x Commercial production  |x Productivity  |x Labor productivity  |x Work quotas  |x Workloads 
650 4 |a Applied sciences  |x Systems science  |x Steady states 
650 4 |a Philosophy  |x Metaphysics  |x Etiology  |x Determinism 
650 4 |a Mathematics 
655 4 |a research-article 
700 1 |a Sigman, Karl  |e verfasserin  |4 aut 
773 0 8 |i Enthalten in  |t Operations Research  |d Institute for Operations Research and the Management Sciences, 1956  |g 46(1998), 3, Seite 378-380  |w (DE-627)320595005  |w (DE-600)2019440-7  |x 15265463  |7 nnns 
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952 |d 46  |j 1998  |e 3  |h 378-380