A discrete-time queueing system with optional LCFS discipline

Atencia, Iván; Pechinkin, A. V.

doi:10.1007/s10479-012-1097-2

Cited by 9 publications

(6 citation statements)

References 12 publications

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“…which is the probability generating function of the system size in the model Geo/G/1/∞ with optional LCFS discipline in (Atencia and Pechinkin 2013).…”

Section: The Markov Chainmentioning

confidence: 99%

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A Discrete-Time Retrial Queueing System With Service Upgrade

Atencia

Ruiz²,

Sánchez³

2015

ECMS 2015 Proceedings Edited By: Valeri M. Mladenov, Petia Georgieva, Grisha Spasov, Galidiya Petrova

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This paper considers a discrete-time retrial queueing system with displacements. The arriving customers can opt to go directly to the server obtaining immediately its service or to join the orbit. In the first case, the displaced customer goes directly to the orbit. The arrivals follow a geometrical law and the service times are general.We study the Markov chain underlying the considered queueing system obtaining the generating function of the number of customers in the orbit and in the system as well as the stationary distribution of the time that a customer spends in the server. We derive the stochastic decomposition law and as an application we give bounds for the proximity between the steady-state distributions for our queueing system and its corresponding standard system.

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“…which is the probability generating function of the system size in the model Geo/G/1/∞ with optional LCFS discipline in (Atencia and Pechinkin 2013).…”

Section: The Markov Chainmentioning

confidence: 99%

“…Works related to discrete-time systems with server interruptions with or without expulsions and vacations can be found, including those by (Fiems et al 2002;Vinck and Bruneel 2006;Morozov et al 2011) as well as (Atencia and Pechinkin 2013;Atencia et al 2013a;2013b;Atencia 2014).…”

Section: Introductionmentioning

confidence: 99%

A Discrete-Time Retrial Queueing System With Service Upgrade

Atencia

Ruiz²,

Sánchez³

2015

ECMS 2015 Proceedings Edited By: Valeri M. Mladenov, Petia Georgieva, Grisha Spasov, Galidiya Petrova

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“…In that paper, they obtained the steady probability of the system by using the recursive method. Atencia and Pechinkin [12] studied the discrete-time queueing system under the optional LCFS discipline in 2013. Wu et al [13] analyzed the discrete-time retrial queueing system with preferred and impatient customers in 2013.…”

Section: Introductionmentioning

confidence: 99%

A Discrete-Time Queue with Preferred Customers and Partial Buffer Sharing

Zhou

Liu

2015

Mathematical Problems in Engineering

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We analyze a discrete-time Geo/Geo/1 queueing system with preferred customers and partial buffer sharing. In this model, customers arrive according to geometrical arrival processes with probabilityλ. If an arriving customer finds the server idle, he begins instantly his services. Otherwise, if the server is busy at the arrival epoch, the arrival either interrupts the customer being served to commence his own service with probabilityθ(the customer is called the preferred customer) or joins the waiting line at the back of the queue with probabilityθ~(the customer is called the normal customer) if permitted. The interrupted customer joins the waiting line at the head of the queue. If the total number of customers in the system is equal to or more than thresholdN, the normal customer will be ignored to enter into the system. But this restriction is not suitable for the preferred customers; that is, this system never loses preferred customers. A necessary and sufficient condition for the system to be stable is investigated and the stationary distribution of the queue length of the system is also obtained. Further, we develop a novel method to solve the probability generating function of the busy period of the system. The distribution of sojourn time of a customer in the server and the other indexes are acquired as well.

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“…This mechanism is called a synchronized or triggered motion, see for example (Artalejo 2000) and (Gelenbe and Label 1998) and concerning with inverse order discipline we refer to (Pechinkin and Svischeva 2004), and (Cascone et al 2011). For service interruptions with expulsions we refer to (Atencia and Pechinkin 2012) and (Atencia et al 2013).…”

Section: Introductionmentioning

confidence: 99%

A Discrete-Time Queueing System With Different Types Of Displacement

Atencia¹,

Ruiz²,

Sánchez³

et al. 2013

ECMS 2013 Proceedings Edited By: Webjorn Rekdalsbakken, Robin T. Bye, Houxiang Zhang

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The performance prediction in communication, jobs processing in computers, etc, are always influenced by the customers behavior and the provision of this additional information will be useful in upgrading the service. Our paper is concerned under a loss and trigger protocol where each customer has a service requirement which may depend on the arrival of a positive or negative customer. In our study we consider customer expulsions and different types of customers displacements taking into account or not its past time of service. The main purpose of this work is to spread the discrete-time queueing theory about expulsions and displacement. We provide a unified way to handle the combinations of different conditions such as positive arrival, negative arrival, trigger movements, past time in service, etc.

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A discrete-time queueing system with optional LCFS discipline

Cited by 9 publications

References 12 publications

A Discrete-Time Retrial Queueing System With Service Upgrade

A Discrete-Time Retrial Queueing System With Service Upgrade

A Discrete-Time Queue with Preferred Customers and Partial Buffer Sharing

A Discrete-Time Queueing System With Different Types Of Displacement

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