Single line queue with repeated demands

Farahmand, Kambiz

doi:10.1007/bf02411475

Cited by 84 publications

(33 citation statements)

References 6 publications

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“…With π 0,0 obtained by (12), a characterization of stability is now straightforward. More precisely, requesting π 0,0 to be larger than zero leads to the stability condition for the single-server system,…”

Section: Stability Conditionmentioning

confidence: 99%

“…As such, for j ∈ Z + , π 0,j is given by (12) and (17), π 1,j by (18) and (19), and π 2,j by (20) and (21).…”

Section: Stationary Distributionmentioning

confidence: 99%

“…where we recall that π 0,0 is given by (12), π 1,0 by (18), and π 2,0 by (20). Expression (23) can be obtained from (7), whereas (24) is derived from (3), and (25) from the combination of (2) and (24).…”

Section: Recursive Formulaementioning

confidence: 99%

“…More precisely, although the model presented here does make assumptions on the service order for the queue, constant retrial rate is commonly associated with FCFS ordering in the orbit queue (see e.g. [9,10], and [11,12] for discussion), with only the customer at the head of the queue able to request for service. In this regard, FCFS ordering of incoming call requests may be viewed as a more natural (but not only) way to realize a constant retrial rate.…”

Section: Introductionmentioning

confidence: 99%

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Two Way Communication Retrial Queues with Balanced Call Blending

Phung-Duc

Rogiest

2012

Analytical and Stochastic Modeling Techniques and Applications

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Abstract. In call centers, call blending consists in the mixing of incoming and outgoing call activity. Artalejo and Phung-Duc recently provided an apt model for such a setting, with a two way communication retrial queue. However, by assuming a classical (proportional) retrial rate for the incoming calls, the outgoing call activity is largely blocked when many incoming calls are in orbit, which may be unwanted, especially when outgoing calls are vital to the service offered.In this paper, we assume a balanced way of call blending, through a retrial queue with constant retrial rate for incoming calls. For the single server case (one operator), a generating functions approach enables deriving explicit formulas for the joint stationary distribution of the number of incoming calls and the system state, and also for the factorial moments. This is complemented with a stability analysis, expressions for performance measures, and also recursive formulas, allowing reliable numerical calculation. For the multiserver case (multiple operators), we provide a quasi-birth-and-death process formulation, enabling deriving a sufficient and necessary condition for stability in this case, as well as a numerical recipe to obtain the stationary distribution.

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Section: Stability Conditionmentioning

confidence: 99%

“…As such, for j ∈ Z + , π 0,j is given by (12) and (17), π 1,j by (18) and (19), and π 2,j by (20) and (21).…”

Section: Stationary Distributionmentioning

confidence: 99%

Section: Recursive Formulaementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Two Way Communication Retrial Queues with Balanced Call Blending

Phung-Duc

Rogiest

2012

Analytical and Stochastic Modeling Techniques and Applications

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“…Farahmand [3] analyzes this model in the steady sta te. He obtains a generating functlan far the number of customers In orbit when the channel ls busy and when the charmel 18 free.…”

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confidence: 99%

A retrial model in a nonstationary regime

Vázquez

1996

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In rhis article we analyze a ruadel of a retrial queueing system where customers in the orhit joio a queDe with FCFS discipline. We adopt a nostationary regime. We derive SOrne probabilities using fue theory of semiregenerative processes. We obtaio aD integral estimator for [he blocking probability. We also find lower and upper bounds for the I 1 distance between the probability distributions in aD M/G/l/oo retrial fiadel and the M/G/ll queue at stationary regime. RESUMENEn este articulo analizamos un modelo con reintentos en el enallos clientes en órbita pasan a fonnar parte de una cola con disciplina PIFO. Adoptaremos régimen no estacionario. Obtendremos algunas probabilidades usando la Teoría de procesos Semiregenerativos y un estimador integral para la probabilidad de bloqueo. Por último, mostramos una cota inferior y otra superior para la distancia 1 1 entre la distribución del número de individuos en el sistema en el caso M/GIl con reintentos y el sistema clásico M/G/lIoo en estado estacionario.

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A Retrial Queueing System with Renewal Input and Phase Type Service Time Distribution

Klimenok

2016

Communications in Computer and Information Science

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Single line queue with repeated demands

Cited by 84 publications

References 6 publications

Two Way Communication Retrial Queues with Balanced Call Blending

Two Way Communication Retrial Queues with Balanced Call Blending

A retrial model in a nonstationary regime

A Retrial Queueing System with Renewal Input and Phase Type Service Time Distribution

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