Analysis of GI X /M(n)//N systems with stochastic customer acceptance policy

Ferreira, Fernando; Pacheco, Antònio

doi:10.1007/s11134-007-9057-2

Cited by 4 publications

(6 citation statements)

References 25 publications

(48 reference statements)

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“…Each component π − * j (z) defined as π − * j (z) = ∞ n=1 π − j (n)z n of the VGF π − * (z) given in (17) being convergent in |z| ≤ 1 implies that π − * (z) is convergent in |z| ≤ 1. As…”

Section: Adj[e] Is the Adjoint Matrix Of A Square Matrix E And Det[e]mentioning

confidence: 99%

“…] whose absolute value is less than or equal to one must be the zeros of the numerator of each component of (17).…”

Section: Adj[e] Is the Adjoint Matrix Of A Square Matrix E And Det[e]mentioning

confidence: 99%

“…. , π m (n)], n ≥ 0, at random epoch using the classical argument based on Markov renewal theory as given in Chaudhry and Templeton [16, p. 74-77], and Ferreira and Pacheco [17], which relates the steady-state system-length distribution at random epoch to that at the corresponding prearrival epoch.…”

Section: System-length Distribution At Random Epochmentioning

confidence: 99%

See 2 more Smart Citations

Analytic and computational analysis of the discrete-time GI/D-MSP/1 queue using roots

Samanta

Chaudhry

Pacheco

et al. 2015

Computers & Operations Research

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Section: Adj[e] Is the Adjoint Matrix Of A Square Matrix E And Det[e]mentioning

confidence: 99%

“…] whose absolute value is less than or equal to one must be the zeros of the numerator of each component of (17).…”

Section: Adj[e] Is the Adjoint Matrix Of A Square Matrix E And Det[e]mentioning

confidence: 99%

See 1 more Smart Citation

Analytic and computational analysis of the discrete-time GI/D-MSP/1 queue using roots

Samanta

Chaudhry

Pacheco

et al. 2015

Computers & Operations Research

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“…, π m (n)], n ≥ 0, at an arbitrary epoch using the classical argument based on Markov renewal theory as given in Chaudhry and Templeton [9, pp. 74-77], and Ferreira and Pacheco [13], which relates the steady-state systemlength distribution at an arbitrary epoch to that at the corresponding prearrival epoch.…”

Section: System-length Distribution At An Arbitrary Epochmentioning

confidence: 99%

“…The steady-state system-length distributions at various epochs and sojourn-time distribution of an arriving customer can be obtained along the same lines as discussed in Section 3. For this, we need to replace S n and n in (13) and (24), respectively, with the results given in this section.…”

Section: The Model With Idle-restart Service Phase Distributionmentioning

confidence: 99%

ANALYTICALLY EXPLICIT RESULTS FOR THE GI/C-MSP/1/∞ QUEUEING SYSTEM USING ROOTS

Chaudhry

Samanta

Pacheco

2012

Prob. Eng. Inf. Sci.

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In this paper, we present (in terms of roots) a simple closed-form analysis for evaluating system-length distribution at prearrival epochs of the GI/C-MSP/1 queue. The proposed analysis is based on roots of the associated characteristic equation of the vector-generating function of system-length distribution. We also provide the steady-state system-length distribution at an arbitrary epoch by using the classical argument based on Markov renewal theory. The sojourn-time distribution has also been investigated. The prearrival epoch probabilities have been obtained using the method of roots which is an alternative approach to the matrix-geometric method and the spectral method. Numerical aspects have been tested for a variety of arrival- and service-time distributions and a sample of numerical outputs is presented. The proposed method not only gives an alternative solution to the existing methods, but it is also analytically simple, easy to implement, and computationally efficient. It is hoped that the results obtained will prove beneficial to both theoreticians and practitioners.

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Numbers of Served and Lost Customers in Busy-Periods of M/M/1/n Systems with Balking

Ferreira

Pacheco

Ribeiro

2020

Computational Science and Its Applications – ICCSA 2020

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In this work we analyze single server Markovian queueing systems with finite capacity and balking, that is M / M /1/ n systems with balking. In these systems, the admission of customers is modulated by the state of the system at the instants of customer arrivals. Depending on the size of the queue upon arrival, customers that find place to join the system decide to enter the system with a certain probability. The number of customers in the system amounts to a Markov chain whose transition probabilities incorporate the balking probabilities. Using the Markovian regenerative property of the chain embedded at the instants of arrival or departure of customers, we characterize the joint probability distribution of the number of customers served and the number of customers lost in busy-periods, that is, during continuous occupation periods of the server. This is accomplished implementing a priori a recursive algorithmic procedure for computing the respective probability-generating function. Finally, a numerical illustration of the derived results is presented for different balking policies.

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Analysis of GI X /M(n)//N systems with stochastic customer acceptance policy

Cited by 4 publications

References 25 publications

Analytic and computational analysis of the discrete-time GI/D-MSP/1 queue using roots

Analytic and computational analysis of the discrete-time GI/D-MSP/1 queue using roots

ANALYTICALLY EXPLICIT RESULTS FOR THE GI/C-MSP/1/∞ QUEUEING SYSTEM USING ROOTS

Numbers of Served and Lost Customers in Busy-Periods of M/M/1/n Systems with Balking

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