A study on state dependent single server queue with Markov modulated arrival under hyper exponential service times using block matrix structured approach
In this research work we study the correlation impact between the inter arrival time and service time of packets arriving to the system for transmission. By assuming the arrival in modulated form the service utilization provided by server acts with varying rate of service. The queuing quantities are...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-03-01
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| Series: | Ain Shams Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2090447925000346 |
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| author | Raghavendran. R V. Vidhya |
| author_facet | Raghavendran. R V. Vidhya |
| author_sort | Raghavendran. R |
| collection | DOAJ |
| description | In this research work we study the correlation impact between the inter arrival time and service time of packets arriving to the system for transmission. By assuming the arrival in modulated form the service utilization provided by server acts with varying rate of service. The queuing quantities are obtained in closed form by using matrix geometric method. The expected waiting length of packets and other performance measures are calculated in the stationary state distribution of the process. We establish the analytic frame work of the Markov model between the inter arrival and service time to get correlation impact to study the behavioural effect in queue length, time and other performance measures. |
| format | Article |
| id | doaj-art-3bf80fd26ff2401cbb3c2abf422cb0b9 |
| institution | Kabale University |
| issn | 2090-4479 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Ain Shams Engineering Journal |
| spelling | doaj-art-3bf80fd26ff2401cbb3c2abf422cb0b92025-02-07T04:47:26ZengElsevierAin Shams Engineering Journal2090-44792025-03-01163103293A study on state dependent single server queue with Markov modulated arrival under hyper exponential service times using block matrix structured approachRaghavendran. R0V. Vidhya1Department of Mathematics School of Advanced Sciences VIT-Chennai IndiaCorresponding author.; Department of Mathematics School of Advanced Sciences VIT-Chennai IndiaIn this research work we study the correlation impact between the inter arrival time and service time of packets arriving to the system for transmission. By assuming the arrival in modulated form the service utilization provided by server acts with varying rate of service. The queuing quantities are obtained in closed form by using matrix geometric method. The expected waiting length of packets and other performance measures are calculated in the stationary state distribution of the process. We establish the analytic frame work of the Markov model between the inter arrival and service time to get correlation impact to study the behavioural effect in queue length, time and other performance measures.http://www.sciencedirect.com/science/article/pii/S2090447925000346Markov modulated arrivalHyper-exponential distributionQuasi-birth-death processMatrix geometric methodStationary vector distribution |
| spellingShingle | Raghavendran. R V. Vidhya A study on state dependent single server queue with Markov modulated arrival under hyper exponential service times using block matrix structured approach Ain Shams Engineering Journal Markov modulated arrival Hyper-exponential distribution Quasi-birth-death process Matrix geometric method Stationary vector distribution |
| title | A study on state dependent single server queue with Markov modulated arrival under hyper exponential service times using block matrix structured approach |
| title_full | A study on state dependent single server queue with Markov modulated arrival under hyper exponential service times using block matrix structured approach |
| title_fullStr | A study on state dependent single server queue with Markov modulated arrival under hyper exponential service times using block matrix structured approach |
| title_full_unstemmed | A study on state dependent single server queue with Markov modulated arrival under hyper exponential service times using block matrix structured approach |
| title_short | A study on state dependent single server queue with Markov modulated arrival under hyper exponential service times using block matrix structured approach |
| title_sort | study on state dependent single server queue with markov modulated arrival under hyper exponential service times using block matrix structured approach |
| topic | Markov modulated arrival Hyper-exponential distribution Quasi-birth-death process Matrix geometric method Stationary vector distribution |
| url | http://www.sciencedirect.com/science/article/pii/S2090447925000346 |
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