Repairable queue with non-exponential service time and variable breakdown rates
Consider a single server queue in which the service station may breakdown according to a Poisson process with rates γ in busy time and γ’ in idle time respectively. After a breakdown, the service station will be repaired immediately and the repair time is assumed to have an exponential distribution...
| Main Authors: | , , |
|---|---|
| Format: | Book Section |
| Language: | English |
| Published: |
AIP Publishing
2015
|
| Subjects: | |
| Online Access: | http://eprints.sunway.edu.my/311/ http://eprints.sunway.edu.my/311/1/Repairable_Queue_AIP_Proceedings_2015.pdf |
| _version_ | 1848801797851840512 |
|---|---|
| author | Koh, Siew Khew Pooi, Ah Hin * Tan, Yi Fei |
| author_facet | Koh, Siew Khew Pooi, Ah Hin * Tan, Yi Fei |
| author_sort | Koh, Siew Khew |
| building | SU Institutional Repository |
| collection | Online Access |
| description | Consider a single server queue in which the service station may breakdown according to a Poisson process with rates γ in busy time and γ’ in idle time respectively. After a breakdown, the service station will be repaired immediately and the repair time is assumed to have an exponential distribution with rate δ. Suppose the arrival time has
an exponential distribution with rate λ, and the probability density function g(t) and the cumulative distribution function G(t) of the service time are such that the rate g(t)/[1 – G(t)] tends to a constant as t tends to infinity. When the queue is in a stationary state, we derive a set of equations for the probabilities of the queue length and the states of the arrival and service processes. Solving the equations, we obtain approximate results for the stationary probabilities which can be used
to obtain the stationary queue length distribution of the system |
| first_indexed | 2025-11-14T21:13:10Z |
| format | Book Section |
| id | sunway-311 |
| institution | Sunway University |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T21:13:10Z |
| publishDate | 2015 |
| publisher | AIP Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | sunway-3112019-03-13T03:37:48Z http://eprints.sunway.edu.my/311/ Repairable queue with non-exponential service time and variable breakdown rates Koh, Siew Khew Pooi, Ah Hin * Tan, Yi Fei QA75 Electronic computers. Computer science Consider a single server queue in which the service station may breakdown according to a Poisson process with rates γ in busy time and γ’ in idle time respectively. After a breakdown, the service station will be repaired immediately and the repair time is assumed to have an exponential distribution with rate δ. Suppose the arrival time has an exponential distribution with rate λ, and the probability density function g(t) and the cumulative distribution function G(t) of the service time are such that the rate g(t)/[1 – G(t)] tends to a constant as t tends to infinity. When the queue is in a stationary state, we derive a set of equations for the probabilities of the queue length and the states of the arrival and service processes. Solving the equations, we obtain approximate results for the stationary probabilities which can be used to obtain the stationary queue length distribution of the system AIP Publishing 2015 Book Section PeerReviewed text en http://eprints.sunway.edu.my/311/1/Repairable_Queue_AIP_Proceedings_2015.pdf Koh, Siew Khew and Pooi, Ah Hin * and Tan, Yi Fei (2015) Repairable queue with non-exponential service time and variable breakdown rates. In: Proceedings of International Conference on Mathematics, Engineering and Industrial Applications 2014 (ICoMEIA 2014) (28–30 May 2014), Penang, Malaysia. AIP Conference Proceedings (1660). AIP Publishing, Melville, NY, 050026-1. doi: 10.1063/1.4915659 |
| spellingShingle | QA75 Electronic computers. Computer science Koh, Siew Khew Pooi, Ah Hin * Tan, Yi Fei Repairable queue with non-exponential service time and variable breakdown rates |
| title | Repairable queue with non-exponential service time and
variable breakdown rates |
| title_full | Repairable queue with non-exponential service time and
variable breakdown rates |
| title_fullStr | Repairable queue with non-exponential service time and
variable breakdown rates |
| title_full_unstemmed | Repairable queue with non-exponential service time and
variable breakdown rates |
| title_short | Repairable queue with non-exponential service time and
variable breakdown rates |
| title_sort | repairable queue with non-exponential service time and
variable breakdown rates |
| topic | QA75 Electronic computers. Computer science |
| url | http://eprints.sunway.edu.my/311/ http://eprints.sunway.edu.my/311/ http://eprints.sunway.edu.my/311/1/Repairable_Queue_AIP_Proceedings_2015.pdf |