On Numerical Computations of Some Discrete-Time Queues

Chaudhry, M. L.

doi:10.1007/978-1-4757-4828-4_10

Cited by 19 publications

(12 citation statements)

References 69 publications

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“…1. The detailed discussion about these concepts has been explained in the past at several places, see, e.g., Hunter (1983); Bruneel and Kim (1993) or Chaudhry (2000). The times between successive arrivals are independent and identically distributed random variables T 1 , T 2 , .…”

Section: Description Of the Model Definitions And Notationsmentioning

confidence: 99%

Analysis of stationary discrete-time GI/D-MSP/1 queue with finite and infinite buffers

2008

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This paper considers a single-server queueing model with finite and infinite buffers in which customers arrive according to a discrete-time renewal process. The customers are served one at a time under discrete-time Markovian service process (D-MSP). This service process is similar to the discrete-time Markovian arrival process (D-MAP), where arrivals are replaced with service completions. Using the imbedded Markov chain technique and the matrix-geometric method, we obtain the system-length distribution at a prearrival epoch. We also provide the steady-state system-length distribution at an arbitrary epoch by using the supplementary variable technique and the classical argument based on renewal-theory. The analysis of actualwaiting-time (in the queue) distribution (measured in slots) has also been investigated. Further, we derive the coefficient of correlation of the lagged interdeparture intervals. Moreover, computational experiences with a variety of numerical results in the form of tables and graphs are discussed.

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Section: Description Of the Model Definitions And Notationsmentioning

confidence: 99%

Analysis of stationary discrete-time GI/D-MSP/1 queue with finite and infinite buffers

2008

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“…! The detailed discussion about these concepts has been explained in the past at several places, see, e.g., Hunter [8] or Chaudhry [5]. We assume that the capacity of the system is N and the inter-arrival times of customers are independent and geometrically distributed with probability mass function (p.m.f.)…”

Section: Model Description and Solutionmentioning

confidence: 99%

Analysis of Discrete-Time Single Server Queue with Balking and Multiple Working Vacations

Laxmi

Goswami

Jyothsna

2013

Quality Technology & Quantitative Management

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______________________________________________________________________ Abstract: This paper analyzes a discrete-time single server queueing system with balking and multiple working vacations. The arriving customers balk (that is, do not join the queue) with a probability. The inter-arrival times of customers are assumed to be independent and geometrically distributed. The server works at a different rate rather than completely stopping service during vacations. The service times during a service period, service times during a vacation period and vacation times are assumed to be geometrically distributed. We obtain the closed form expressions for the steady-state probabilities at arbitrary and outside observer's observation epochs. Computational experiences with a variety of numerical results are discussed in the form of tables and graphs. Moreover, some queueing models discussed in the literature are derived as special cases of our model.

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“…Systems where time is slotted include asynchronous transfer mode (AT M), ALOH A protocol, time-division multiple access (T DMA) and others. Interested readers are referred to the selected references (Bruneel and Kim 1993;Chaudhry 2000;Rom and Sidi 1990;Takagi 1993) for further motivation and a comprehensive review.…”

Section: Introductionmentioning

confidence: 99%

Performance Analysis of a Block-Structured Discrete-Time Retrial Queue with State-Dependent Arrivals

Artalejo

2009

Discrete Event Dyn Syst

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In this paper, we introduce a new discrete block state-dependent arrival (D-BSDA) distribution which provides fresh insights leading to a successful generalization of the discrete-time Markovian arrival process (D-MAP). The D-BSDA distribution is related to structured Markov chains and the method of stages. The consideration of this new discrete-time state-dependent block description gives one the ability of construct new stochastic models. The retrial queue analyzed in this paper gives an example of application of the D-BSDA distribution to construct more general and sophisticated models. We assume that the primary arrivals and the retrials follow the D-BSDA description and the service times are of discrete phasetype (PH). We study the underlying level dependent Markov chain of M/G/1-type at the epochs immediately after the slot boundaries. To this end, we employ the ULtype RG-factorization which provides an expression for the stationary probabilities. We also perform an analysis of waiting times. Numerical experiments are presented to study the system performance.

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On Numerical Computations of Some Discrete-Time Queues

Cited by 19 publications

References 69 publications

Analysis of stationary discrete-time GI/D-MSP/1 queue with finite and infinite buffers

Analysis of stationary discrete-time GI/D-MSP/1 queue with finite and infinite buffers

Analysis of Discrete-Time Single Server Queue with Balking and Multiple Working Vacations

Performance Analysis of a Block-Structured Discrete-Time Retrial Queue with State-Dependent Arrivals

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