A queueing model for a terminal system subject to breakdowns
The queueing system to be analysed is a model of a terminal system subject to random breakdowns. All random variables involved here are independent and exponentially distributed. Although, the stochastic process describing the system's behaviour is a Markov chain, the number of states becomes v...
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| Published in | Computers & mathematics with applications (1987) Vol. 19; no. 1; pp. 143 - 147 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Oxford
Elsevier Ltd
1990
Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0898-1221 1873-7668 |
| DOI | 10.1016/0898-1221(90)90094-Z |
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| Abstract | The queueing system to be analysed is a model of a terminal system subject to random breakdowns. All random variables involved here are independent and exponentially distributed. Although, the stochastic process describing the system's behaviour is a Markov chain, the number of states becomes very large. Therefore, our aim is to give a recursive scheme for the solution of the steady-state equations. In equilibrium, the main performance measures of the system, such as mean number of jobs staying at the CPU, the mean number of good terminals, the average number of busy servers, the expected response times of jobs, and utilizations are obtained. Finally, some numerical results illustrate the problem in question. |
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| AbstractList | The queueing system to be analysed is a model of a terminal system subject to random breakdowns. All random variables involved here are independent and exponentially distributed. Although, the stochastic process describing the system's behaviour is a Markov chain, the number of states becomes very large. Therefore, our aim is to give a recursive scheme for the solution of the steady-state equations. In equilibrium, the main performance measures of the system, such as mean number of jobs staying at the CPU, the mean number of good terminals, the average number of busy servers, the expected response times of jobs, and utilizations are obtained. Finally, some numerical results illustrate the problem in question. |
| Author | Gál, T. Sztrik, J. |
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| Cites_doi | 10.1287/opre.33.1.183 |
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| Copyright | 1990 1990 INIST-CNRS |
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| EndPage | 147 |
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| Keywords | Performance evaluation Multiprogramming Computer system Failures Modeling Random event Queuing system |
| Language | English |
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| References | Gelenbe, Mitrani (BIB2) 1980 Tijms (BIB9) 1986 Kleinrock (BIB4) 1976 Gross, Harris (BIB3) 1985 Sztrik (BIB8) 1986; 7 Feller (BIB1) 1950 (BIB5) 1983 Sztrik (BIB7) 1984; 7 Snyder, Stewart (BIB6) 1985; 33 Sztrik (10.1016/0898-1221(90)90094-Z_BIB8) 1986; 7 Gross (10.1016/0898-1221(90)90094-Z_BIB3) 1985 Sztrik (10.1016/0898-1221(90)90094-Z_BIB7) 1984; 7 Gelenbe (10.1016/0898-1221(90)90094-Z_BIB2) 1980 Kleinrock (10.1016/0898-1221(90)90094-Z_BIB4) 1976 (10.1016/0898-1221(90)90094-Z_BIB5) 1983 Feller (10.1016/0898-1221(90)90094-Z_BIB1) 1950 Snyder (10.1016/0898-1221(90)90094-Z_BIB6) 1985; 33 Tijms (10.1016/0898-1221(90)90094-Z_BIB9) 1986 |
| References_xml | – volume: 7 start-page: 127 year: 1984 end-page: 135 ident: BIB7 article-title: A queueing model for multiprogrammed computer systems with different I/O times publication-title: Acta Cybernetica – year: 1986 ident: BIB9 article-title: Stochastical Modelling and Analysis, A Computational Approach – year: 1950 ident: BIB1 publication-title: An Introduction to Probability Theory and its Applications Vol. I – year: 1983 ident: BIB5 publication-title: Computer Performance Modeling Handbook – volume: 33 start-page: 183 year: 1985 end-page: 202 ident: BIB6 article-title: Explicit and iterative approaches to solving queueing models publication-title: Opns. Res. – year: 1976 ident: BIB4 article-title: Queueing Systems, Vol. II, Computer Applications – volume: 7 start-page: 329 year: 1986 end-page: 340 ident: BIB8 article-title: A probability model for priority processor-shared multiprogrammed computer systems publication-title: Acta Cybernetica – year: 1980 ident: BIB2 article-title: Analysis and Synthesis of Computer Systems – year: 1985 ident: BIB3 article-title: Fundamentals of Queueing Theory – year: 1976 ident: 10.1016/0898-1221(90)90094-Z_BIB4 – volume: 33 start-page: 183 year: 1985 ident: 10.1016/0898-1221(90)90094-Z_BIB6 article-title: Explicit and iterative approaches to solving queueing models publication-title: Opns. Res. doi: 10.1287/opre.33.1.183 – volume: 7 start-page: 329 year: 1986 ident: 10.1016/0898-1221(90)90094-Z_BIB8 article-title: A probability model for priority processor-shared multiprogrammed computer systems publication-title: Acta Cybernetica – year: 1950 ident: 10.1016/0898-1221(90)90094-Z_BIB1 – year: 1986 ident: 10.1016/0898-1221(90)90094-Z_BIB9 – year: 1983 ident: 10.1016/0898-1221(90)90094-Z_BIB5 – volume: 7 start-page: 127 year: 1984 ident: 10.1016/0898-1221(90)90094-Z_BIB7 article-title: A queueing model for multiprogrammed computer systems with different I/O times publication-title: Acta Cybernetica – year: 1980 ident: 10.1016/0898-1221(90)90094-Z_BIB2 – year: 1985 ident: 10.1016/0898-1221(90)90094-Z_BIB3 |
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| Title | A queueing model for a terminal system subject to breakdowns |
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