Transient product from distributions in queueing networks

Boucherie, Richard J.; Taylor, Peter G.

doi:10.1007/bf01439160

Cited by 21 publications

(19 citation statements)

References 22 publications

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“…As detailed in Boucherie and Taylor (1993), ρ i (t), i = 1, 2, ..., n is the solution to the following linear differential equation:…”

Section: Detailed State Probability Distribution Of Infinite Servers mentioning

confidence: 99%

Detailed state probability distribution of infinite servers queues with phase-type distributed service times

Mura¹

2015

Ontare

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We present a detailed analysis of the M/PH/ queue, which allows determining an analytic form for both the transient and the steady-state probability distribution of customers at the various phases of the service. The analysis is based on the correspondence that can be found between the stochastic process representing the number of customers in service at the various phases of the PH distribution, and a stochastic process that represents the evolution of the number of customers in the nodes of a Jackson's network where all service centers are M/M/ queues. Keywords

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“…As detailed in Boucherie and Taylor (1993), ρ i (t), i = 1, 2, ..., n is the solution to the following linear differential equation:…”

Section: Detailed State Probability Distribution Of Infinite Servers mentioning

confidence: 99%

Detailed state probability distribution of infinite servers queues with phase-type distributed service times

Mura¹

2015

Ontare

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“…In some cases, even if the state space is large, special characteristics can be exploited to carry out an exact analysis. Such situations are limited in practice to networks of infinite server queues [4,14]. Consequently, we most often must settle for an approximate solution.…”

Section: Introductionmentioning

confidence: 99%

Approximate Transient Analysis of Queuing Networks by Decomposition based on Time-Inhomogeneous Markov Arrival Processes

Angius¹,

Horváth²

2015

Proceedings of the 8th International Conference on Performance Evaluation Methodologies and Tools

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We address the transient analysis of networks of queues with exponential service times. Such networks can easily have such a huge state space that their exact transient analysis is unfeasible.In this paper we propose an approximate transient analysis technique based on decomposing the queues of the network using a compact and approximate representation of the departure process of each queue. Namely, we apply time-inhomogeneous Markov arrival processes (IMAP) to describe the stream of clients leaving the queues. By doing so, the overall approximate model of the network is a time-inhomogeneous continuous time Markov chain (ICTMC) with significantly less number of states than there are in the original Markov chain.The proposed construction of the output IMAP of a queue is based on its transient state probabilities. We illustrate the approach first on a single M/M/1 queue and analyze the goodness of fitting of the departure process by numerical examples. Then we extend the approach to networks of queues and evaluate the precision of the resulting technique on several simple numerical examples by comparing the exact and the approximate transient probabilities of the queues.

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“…, c N satisfy (7), (8), and (9). Conversely, if P(n, t ) is of the form (10), then insertion in the forward equations (11) implies (7), (8), and (9).…”

Section: Model and Technical Lemmamentioning

confidence: 99%

“…[26] to queueing networks consisting of infinite-server queues in the more general context of Poisson arrival location models. In Boucherie and Taylor [8] , it is shown that the only single-routing queueing networks that have transient product-form distribution are networks of infinite server queues. For two particular clustering processes for polymers with a treelike structure that have reaction rates proportional to the size of the polymers, the transient distribution is shown to be of product form [10,11] .…”

Section: Reaction Network and Product Form In The Literaturementioning

confidence: 99%

Transient detailed balance and product form for reaction networks

Boer

Boucherie

2017

Stochastic Models

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This paper explores the boundary of the set of reaction networks that have an exact transient (truncated) multidimensional Poisson or product-form distribution for the number of particles of different types. Motivated by the birth-death process, we introduce the notions of transient detailed balance and delay functions, and use these notions to obtain the novel transient product-form distribution in a coagulation-fragmentation process for polymers with a tree-like structure from that of the pure coagulation process.

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Transient product from distributions in queueing networks

Abstract: In this paper it is shown that a necessary and sufficiënt condition for a Markovian queueing network to have transient product form is that all queues are infmite server queues.

Cited by 21 publications

References 22 publications

Detailed state probability distribution of infinite servers queues with phase-type distributed service times

Detailed state probability distribution of infinite servers queues with phase-type distributed service times

Approximate Transient Analysis of Queuing Networks by Decomposition based on Time-Inhomogeneous Markov Arrival Processes

Transient detailed balance and product form for reaction networks

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