Maintenance of deteriorating non-exponential single server queue / Koh Siew Khew
Consider the single server queue in which the system capacity is infinite and the customers are served on a first come, first served basis. The case of a system without deterioration is first studied. The stationary queue length distribution and the stationary waiting time distribution are derive...
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| Format: | Thesis |
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2013
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| Online Access: | http://studentsrepo.um.edu.my/4160/ http://studentsrepo.um.edu.my/4160/1/MAINTENANCE_OF_DETERIORATING_NON%2DEXPONENTIAL_SINGLE_SERVER_QUEUE.pdf |
| _version_ | 1848772578063155200 |
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| author | Koh, Siew Khew |
| author_facet | Koh, Siew Khew |
| author_sort | Koh, Siew Khew |
| building | UM Research Repository |
| collection | Online Access |
| description | Consider the single server queue in which the system capacity is infinite and the
customers are served on a first come, first served basis. The case of a system without
deterioration is first studied. The stationary queue length distribution and the stationary
waiting time distribution are derived for the system in which the service time and
interarrival time distributions are assumed to have constant asymptotic rates. The results
found are verified by using simulation. Next consider a system in which the server would
deteriorate due to random shocks and the seriously affected server will be sent for repair. A
similar method is applied for deriving the stationary queue length distribution in a system
in which the interarrival time distribution (or service time) is assumed to have a constant
asymptotic rate while the service time (or interarrival time) remains exponentially
distributed. From the stationary queue length distribution, a number of other characteristics
can be derived. These include the sojourn time distribution of a customer who arrives when
the queue is in a stationary state, and the expected length of the duration between two
successive repair completions. From these distributions and expected length, the value of
the specified maintenance level is found such that the long run average cost is minimized. |
| first_indexed | 2025-11-14T13:28:44Z |
| format | Thesis |
| id | um-4160 |
| institution | University Malaya |
| institution_category | Local University |
| last_indexed | 2025-11-14T13:28:44Z |
| publishDate | 2013 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | um-41602014-10-13T01:55:42Z Maintenance of deteriorating non-exponential single server queue / Koh Siew Khew Koh, Siew Khew Q Science (General) QA Mathematics Consider the single server queue in which the system capacity is infinite and the customers are served on a first come, first served basis. The case of a system without deterioration is first studied. The stationary queue length distribution and the stationary waiting time distribution are derived for the system in which the service time and interarrival time distributions are assumed to have constant asymptotic rates. The results found are verified by using simulation. Next consider a system in which the server would deteriorate due to random shocks and the seriously affected server will be sent for repair. A similar method is applied for deriving the stationary queue length distribution in a system in which the interarrival time distribution (or service time) is assumed to have a constant asymptotic rate while the service time (or interarrival time) remains exponentially distributed. From the stationary queue length distribution, a number of other characteristics can be derived. These include the sojourn time distribution of a customer who arrives when the queue is in a stationary state, and the expected length of the duration between two successive repair completions. From these distributions and expected length, the value of the specified maintenance level is found such that the long run average cost is minimized. 2013 Thesis NonPeerReviewed application/pdf http://studentsrepo.um.edu.my/4160/1/MAINTENANCE_OF_DETERIORATING_NON%2DEXPONENTIAL_SINGLE_SERVER_QUEUE.pdf Koh, Siew Khew (2013) Maintenance of deteriorating non-exponential single server queue / Koh Siew Khew. PhD thesis, University of Malaya. http://studentsrepo.um.edu.my/4160/ |
| spellingShingle | Q Science (General) QA Mathematics Koh, Siew Khew Maintenance of deteriorating non-exponential single server queue / Koh Siew Khew |
| title | Maintenance of deteriorating non-exponential single server queue / Koh Siew Khew |
| title_full | Maintenance of deteriorating non-exponential single server queue / Koh Siew Khew |
| title_fullStr | Maintenance of deteriorating non-exponential single server queue / Koh Siew Khew |
| title_full_unstemmed | Maintenance of deteriorating non-exponential single server queue / Koh Siew Khew |
| title_short | Maintenance of deteriorating non-exponential single server queue / Koh Siew Khew |
| title_sort | maintenance of deteriorating non-exponential single server queue / koh siew khew |
| topic | Q Science (General) QA Mathematics |
| url | http://studentsrepo.um.edu.my/4160/ http://studentsrepo.um.edu.my/4160/1/MAINTENANCE_OF_DETERIORATING_NON%2DEXPONENTIAL_SINGLE_SERVER_QUEUE.pdf |