New Approach for Finding Basic Performance Measures of Single Server Queue
Consider the single server queue in which the system capacity is infinite and the customers are served on a first come, first served basis. Suppose the probability density function f(t) and the cumulative distribution function F(t) of the interarrival time are such that the rate f(t)/1-F(t) tends to...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2014/851738 |
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| author | Siew Khew Koh Ah Hin Pooi Yi Fei Tan |
| author_facet | Siew Khew Koh Ah Hin Pooi Yi Fei Tan |
| author_sort | Siew Khew Koh |
| collection | DOAJ |
| 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. Suppose the probability density function f(t) and the cumulative distribution function F(t) of the interarrival time are such that the rate f(t)/1-F(t) tends to a constant as t→∞, and the rate computed from the distribution of the service time tends to another constant. 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 and waiting time distribution of a customer who arrives when the queue is in the stationary state. |
| format | Article |
| id | doaj-art-9e5c450af72549ab9307ffbd4b742d8e |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-9e5c450af72549ab9307ffbd4b742d8e2025-02-03T01:30:51ZengWileyJournal of Probability and Statistics1687-952X1687-95382014-01-01201410.1155/2014/851738851738New Approach for Finding Basic Performance Measures of Single Server QueueSiew Khew Koh0Ah Hin Pooi1Yi Fei Tan2Faculty of Engineering and Sciences, Universiti Tunku Abdul Rahman, Jalan Genting Kelang, 53300 Setapak, Wilayah Persekutuan, MalaysiaSunway University Business School, Sunway University, 47500 Subang Jaya, Selangor, MalaysiaFaculty of Engineering, Multimedia University, 63100 Cyberjaya, Selangor, MalaysiaConsider the single server queue in which the system capacity is infinite and the customers are served on a first come, first served basis. Suppose the probability density function f(t) and the cumulative distribution function F(t) of the interarrival time are such that the rate f(t)/1-F(t) tends to a constant as t→∞, and the rate computed from the distribution of the service time tends to another constant. 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 and waiting time distribution of a customer who arrives when the queue is in the stationary state.http://dx.doi.org/10.1155/2014/851738 |
| spellingShingle | Siew Khew Koh Ah Hin Pooi Yi Fei Tan New Approach for Finding Basic Performance Measures of Single Server Queue Journal of Probability and Statistics |
| title | New Approach for Finding Basic Performance Measures of Single Server Queue |
| title_full | New Approach for Finding Basic Performance Measures of Single Server Queue |
| title_fullStr | New Approach for Finding Basic Performance Measures of Single Server Queue |
| title_full_unstemmed | New Approach for Finding Basic Performance Measures of Single Server Queue |
| title_short | New Approach for Finding Basic Performance Measures of Single Server Queue |
| title_sort | new approach for finding basic performance measures of single server queue |
| url | http://dx.doi.org/10.1155/2014/851738 |
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