Lattice paths approach for transient solutions of M /G /1 queues using Coxian 2-phase distributio

The paper aims at deriving transient solutions of non- Markovian queuing system M/G/1 starting from (k,0) to (m,n),m > n remaining below the barrier Y = X and does not include any idle time of server through lattice path approach. The explicit form of the density and other measures of the sys...

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Main Authors: Slamet, I., Gupta, Ritu, Achuthan, N., Collinson, Roger
Format: Journal Article
Published: North Atlantic University Union 2016
Online Access:http://hdl.handle.net/20.500.11937/58292
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author Slamet, I.
Gupta, Ritu
Achuthan, N.
Collinson, Roger
author_facet Slamet, I.
Gupta, Ritu
Achuthan, N.
Collinson, Roger
author_sort Slamet, I.
building Curtin Institutional Repository
collection Online Access
description The paper aims at deriving transient solutions of non- Markovian queuing system M/G/1 starting from (k,0) to (m,n),m > n remaining below the barrier Y = X and does not include any idle time of server through lattice path approach. The explicit form of the density and other measures of the system performance are not known. Our approach is to approximate general service time with Coxian 2-phase distribution, C2 and represent the queuing process as a lattice path by recording the state of the system at the point of transitions. We use the lattice path combinatorics to count the feasible number of paths and corresponding probabilities. The above leads to the required density that has simple probabilistic structure and can be computed using R .The investigation of the influence of taking different values of a parameter on the behavior of the graphs of the density is also presented.
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format Journal Article
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institution Curtin University Malaysia
institution_category Local University
last_indexed 2025-11-14T10:12:21Z
publishDate 2016
publisher North Atlantic University Union
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spelling curtin-20.500.11937-582922017-11-24T05:24:54Z Lattice paths approach for transient solutions of M /G /1 queues using Coxian 2-phase distributio Slamet, I. Gupta, Ritu Achuthan, N. Collinson, Roger The paper aims at deriving transient solutions of non- Markovian queuing system M/G/1 starting from (k,0) to (m,n),m > n remaining below the barrier Y = X and does not include any idle time of server through lattice path approach. The explicit form of the density and other measures of the system performance are not known. Our approach is to approximate general service time with Coxian 2-phase distribution, C2 and represent the queuing process as a lattice path by recording the state of the system at the point of transitions. We use the lattice path combinatorics to count the feasible number of paths and corresponding probabilities. The above leads to the required density that has simple probabilistic structure and can be computed using R .The investigation of the influence of taking different values of a parameter on the behavior of the graphs of the density is also presented. 2016 Journal Article http://hdl.handle.net/20.500.11937/58292 North Atlantic University Union restricted
spellingShingle Slamet, I.
Gupta, Ritu
Achuthan, N.
Collinson, Roger
Lattice paths approach for transient solutions of M /G /1 queues using Coxian 2-phase distributio
title Lattice paths approach for transient solutions of M /G /1 queues using Coxian 2-phase distributio
title_full Lattice paths approach for transient solutions of M /G /1 queues using Coxian 2-phase distributio
title_fullStr Lattice paths approach for transient solutions of M /G /1 queues using Coxian 2-phase distributio
title_full_unstemmed Lattice paths approach for transient solutions of M /G /1 queues using Coxian 2-phase distributio
title_short Lattice paths approach for transient solutions of M /G /1 queues using Coxian 2-phase distributio
title_sort lattice paths approach for transient solutions of m /g /1 queues using coxian 2-phase distributio
url http://hdl.handle.net/20.500.11937/58292