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...
| Main Authors: | , , , |
|---|---|
| Format: | Journal Article |
| Published: |
North Atlantic University Union
2016
|
| Online Access: | http://hdl.handle.net/20.500.11937/58292 |
| _version_ | 1848760223058100224 |
|---|---|
| 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. |
| first_indexed | 2025-11-14T10:12:21Z |
| format | Journal Article |
| id | curtin-20.500.11937-58292 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:12:21Z |
| publishDate | 2016 |
| publisher | North Atlantic University Union |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 |