Simultaneity in discrete-time single server queues with Bernoulli inputs

Gravey, Annie; Hebuterne, Gérard

doi:10.1016/0166-5316(92)90014-8

Cited by 97 publications

(47 citation statements)

References 2 publications

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“…It is assumed that all queueing activities (arrivals and departures) occur at the slot boundaries, and therefore they may occur at the same time. For mathematical clarity, we will suppose that the departures occur at the moment immediately before the slot boundaries and the arrivals occur at the moment immediately after the slot boundaries; that is, we will discuss the model only for the early arrival system policy (details on this and related concepts can be found in [11,14]). …”

Section: Introductionmentioning

confidence: 99%

A discrete time single-server queue with balking: economic applications

Lozano

Moreno

2008

Applied Economics

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This article studies a discrete time single-server queue with finite and infinite buffer where the users have the option to leave the queue upon arrival (balking). We consider two variants of the model in accordance with the balking policies. Firstly, all the arriving customers balk with a constant probability. Secondly, arriving customers increase their balking probabilities as more customers join the system. Specifically, we find the ergodicity condition and closed-form expressions for the stationary distribution of the system size, of the waiting/spending time in the FCFS system and of the unfinished work. The mathematical model is applied in order to resolve several real-life problems in the economic field; in this sense, practical applications in the secondary and tertiary sector are shown. We also develop a cost model to determine the buffer capacity that minimizes certain cost function and give some numerical examples.

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Section: Introductionmentioning

confidence: 99%

A discrete time single-server queue with balking: economic applications

Lozano

Moreno

2008

Applied Economics

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“…Arrivals first (AF) and departures first (DF) buffer management policies for discrete time queues stipulate how a buffer is filled or emptied in the case of simultaneous arrivals and departures at a boundary epoch of a slot [19]. In such cases, according to AF policy, arrivals take precedence over departures while, under DF policy, the opposite effect is observed (see figure 1).…”

Section: Remarksmentioning

confidence: 99%

“…In such cases, according to AF policy, arrivals take precedence over departures while, under DF policy, the opposite effect is observed (see figure 1). Such buffer management policies may play a significant role in determination of blocking probabilities in discrete time finite capacity queues [19,20]. …”

Section: Remarksmentioning

confidence: 99%

A Product Form Approximation for Arbitrary Discrete Time Networks of Shared Buffer Queues

Kouvatsos

Wilkinson

1995

Performance Modelling and Evaluation of ATM Networks

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A product form approximation, based on the principle of maximum entropy (ME), is characterised for arbitrary open discrete time queueing network models (QNMs) of shared buffer ATM switches under the departures ftrst (DF) buffer management policy. Traffic entering and flowing in the network is assumed to be bursty and is modelled by a Compound Bernoulli Process (CBP) with geometrically distributed bulk sizes. Entropy maximisation implies decomposition of the network into individual shared buffer switches which are analysed to obtain cell loss probabilities and mean delays. The ME queue length distribution of a single shared buffer queue under DF policy, together with closed form expressions for the ftrst two moments of the effective flow, play the role of building blocks in the solution process. Typical numerical results are included to demonstrate the utility and computational efftciency of the ME procedure. Comments on current work, involving discrete time ftnite capacity queues with space priority and correlated traffic, are included.

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“…At each time slot, the following events occur in sequence: departure (if any), positive arrival (if any) and negative arrival (if any); therefore, we will discuss the model for the early arrival system (EAS) policy. Details on the EAS discipline and related concepts can be found in [26,29].…”

Section: The Mathematical Modelmentioning

confidence: 99%

A single-server G-queue in discrete-time with geometrical arrival and service process

Atencia

Moreno

2005

Performance Evaluation

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Negative arrivals are used as a control mechanism in many telecommunication and computer networks. This paper analyses a discrete-time single-server queue with geometrical arrivals of both positive and negative customers. We consider both the cases where negative customers remove positive customers from the front and the end of the queue and, in the latter case, the two sub-cases in which a customer currently being served can and cannot be killed by a negative customer. Thus, we carry out a complete study of these systems, including the ergodicity condition as well as exact formulae for the associated stationary distribution. The effect of several parameters on the systems is shown numerically.

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Simultaneity in discrete-time single server queues with Bernoulli inputs

Cited by 97 publications

References 2 publications

A discrete time single-server queue with balking: economic applications

A discrete time single-server queue with balking: economic applications

A Product Form Approximation for Arbitrary Discrete Time Networks of Shared Buffer Queues

A single-server G-queue in discrete-time with geometrical arrival and service process

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