UnivTrevesV1, PascalFrancis, Curation, bibRecord, 000296

Transient and stationary distributions for the GI/G/k queue with Lebesgue-dominated inter-arrival time distribution

Identifieur interne : 000296 ( PascalFrancis/Curation ); précédent : 000295; suivant : 000297

Transient and stationary distributions for the GI/G/k queue with Lebesgue-dominated inter-arrival time distribution

Auteurs : Lothar Breuer [Allemagne]

Source :

Queueing systems [ 0257-0130 ] ; 2003.

RBID : Pascal:03-0516800

Descripteurs français

Pascal (Inist)
- Méthode analytique, File attente, Méthode matricielle, Probabilité transition, Chaîne Markov, Temps service, Distribution temporelle, Temps arrivée, Condition stationnaire, Temps discret, File n serveurs, File attente M G 1, Matrice Hessenberg.

English descriptors

KwdEn :
- Analytical method, Arrival time, Discrete time, Hessenberg matrix, M G 1 queue, Markov chain, Matrix method, Multiserver queue, Queue, Service time, Stationary condition, Time distribution, Transition probability.

Abstract

In this paper, the multi-server queue with general service time distribution and Lebesgue-dominated iid inter-arival times is analyzed. This is done by introducing auxiliary variables for the remaining service times and then examining the embedded Markov chain at arrival instants. The concept of piecewise-deterministic Markov processes is applied to model the inter-arrival behaviour. It turns out that the transition probability kernel of the embedded Markov chain at arrival instants has the form of a lower Hessenberg matrix and hence admits an operator-geometric stationary distribution. Thus it is shown that matrix-analytical methods can be extended to provide a modeling tool even for the general multi-server queue.

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A64	`01`	`1`		`@0 Queueing systems`
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C01	`01`		`ENG`	@0 In this paper, the multi-server queue with general service time distribution and Lebesgue-dominated iid inter-arival times is analyzed. This is done by introducing auxiliary variables for the remaining service times and then examining the embedded Markov chain at arrival instants. The concept of piecewise-deterministic Markov processes is applied to model the inter-arrival behaviour. It turns out that the transition probability kernel of the embedded Markov chain at arrival instants has the form of a lower Hessenberg matrix and hence admits an operator-geometric stationary distribution. Thus it is shown that matrix-analytical methods can be extended to provide a modeling tool even for the general multi-server queue.
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C03	`06`	`X`	`SPA`	`@0 Tiempo servicio @5 06`
C03	`07`	`X`	`FRE`	`@0 Distribution temporelle @5 07`
C03	`07`	`X`	`ENG`	`@0 Time distribution @5 07`
C03	`07`	`X`	`SPA`	`@0 Distribución temporal @5 07`
C03	`08`	`X`	`FRE`	`@0 Temps arrivée @5 08`
C03	`08`	`X`	`ENG`	`@0 Arrival time @5 08`
C03	`08`	`X`	`SPA`	`@0 Tiempo llegada @5 08`
C03	`09`	`X`	`FRE`	`@0 Condition stationnaire @5 09`
C03	`09`	`X`	`ENG`	`@0 Stationary condition @5 09`
C03	`09`	`X`	`SPA`	`@0 Condición estacionaria @5 09`
C03	`10`	`X`	`FRE`	`@0 Temps discret @5 10`
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C03	`11`	`X`	`FRE`	`@0 File n serveurs @5 11`
C03	`11`	`X`	`ENG`	`@0 Multiserver queue @5 11`
C03	`11`	`X`	`SPA`	`@0 Fila n servidores @5 11`
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C03	`13`	`X`	`FRE`	`@0 Matrice Hessenberg @4 CD @5 97`
C03	`13`	`X`	`ENG`	`@0 Hessenberg matrix @4 CD @5 97`
N21				`@1 342`
N82				`@1 PSI`

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Le document en format XML

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   |texte=   Transient and stationary distributions for the GI/G/k queue with Lebesgue-dominated inter-arrival time distribution
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Transient and stationary distributions for the GI/G/k queue with Lebesgue-dominated inter-arrival time distribution

Transient and stationary distributions for the GI/G/k queue with Lebesgue-dominated inter-arrival time distribution

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Descripteurs français

English descriptors

Abstract

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