An M/PH/k retrial queue with finite number of sources

Alfa, Attahiru Sule; Isotupa, K. P. Sapna

doi:10.1016/s0305-0548(03)00100-x

Cited by 32 publications

(14 citation statements)

References 8 publications

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“…Finite source queueing models are systems in which there is a limited number of customers who use the service offered by the system. Two widely known applications of these models are machine interference (Mittler and Kern, 1997) and computer-communications systems (Alfa and Sapna Isotupa, 2004). For finite source queuing systems applications and bibliography of related papers, see Sztrik (2001).…”

Section: Introductionmentioning

confidence: 99%

Transient Analysis of the M/M/k/N/N Queue using a Continuous Time Homogeneous Markov System with Finite State Size Capacity

Vasiliadis

2014

Communications in Statistics - Theory and Methods

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In this article, the M/M/k/N/N queue is modeled as a continuous-time homogeneousMarkov system with finite state size capacity (HMS/c s ). In order to examine the behavior of the queue a continuous-time homogeneous Markov system (HMS) constituted of two states is used. The first state of this HMS corresponds to the source and the second one to the state with the servers. The second state has a finite capacity which corresponds to the number of servers. The members of the system which can not enter the second state, due to its finite capacity, enter the buffer state which represents the system's queue. In order to examine the variability of the state sizes formulae for their factorial and mixed factorial moments are derived in matrix form. As a consequence, the pmf of each state size can be evaluated for any t ∈ + . The theoretical results are illustrated by a numerical example.

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Section: Introductionmentioning

confidence: 99%

Transient Analysis of the M/M/k/N/N Queue using a Continuous Time Homogeneous Markov System with Finite State Size Capacity

Vasiliadis

2014

Communications in Statistics - Theory and Methods

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“…Nonhomogeneous or level dependent QBDs (LDQBDs), which are often more realistic models, are much more complicated to analyze. Some notable matrix analytic approaches for calculating the stationary distribution of LDQBDs exist [5][6][7][8][9] and have been used in a couple of recent applications [10][11][12][13][14][15], but actually LDQBDs are often solved by techniques for general (not specifically structured) Markov chains [16][17][18] without exploiting the QBD structure.…”

Section: Introductionmentioning

confidence: 99%

Steady state analysis of level dependent quasi-birth-and-death processes with catastrophes

Baumann¹,

Sandmann²

2012

Computers & Operations Research

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“…Alfa and Isotupa [1] studied retrial queues with a finite source of customers and identical multiple servers in parallel. A markovian queue with two heterogeneous servers and multiple vacations was analyzed by Krishna Kumar and Madheswari [2].…”

Section: Introductionmentioning

confidence: 99%

Synchronous working vacation policy for finite-buffer multiserver queueing system

Jain¹,

Upadhyaya²

2011

Applied Mathematics and Computation

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An M/PH/k retrial queue with finite number of sources

Cited by 32 publications

References 8 publications

Transient Analysis of the M/M/k/N/N Queue using a Continuous Time Homogeneous Markov System with Finite State Size Capacity

Transient Analysis of the M/M/k/N/N Queue using a Continuous Time Homogeneous Markov System with Finite State Size Capacity

Steady state analysis of level dependent quasi-birth-and-death processes with catastrophes

Synchronous working vacation policy for finite-buffer multiserver queueing system

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