A recursive solution of a queueing model for a multi-terminal system subject to breakdowns

Sztrik, János; Gál, Tímea

doi:10.1016/0166-5316(90)90023-c

Cited by 23 publications

(9 citation statements)

References 3 publications

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“…To get its steady-state probabilities an efficient recursive computational method has been introduced and used for the different service rules mentioned earlier (see [1][2][3][4]14]). …”

Section: (T) = (X(t) Y(t) Yi(t) Z(t) Zi(t))mentioning

confidence: 99%

“…Assuming again that tile random variables involved are independent and exponentially distributed, different models have been discussed. The homogeneous case, i.e.. when the thinking times, processing times, failure-free operation times, and the restoration times are l.ho same for all terminals, has been dealt with in [14]. The heterogeneous models under PPS.…”

Section: Introductionmentioning

confidence: 99%

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The effects of service disciplines on the performance of a nonreliable terminal system

Almási

Sztrik

1998

J Math Sci

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“…To get its steady-state probabilities an efficient recursive computational method has been introduced and used for the different service rules mentioned earlier (see [1][2][3][4]14]). …”

Section: (T) = (X(t) Y(t) Yi(t) Z(t) Zi(t))mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The effects of service disciplines on the performance of a nonreliable terminal system

Almási

Sztrik

1998

J Math Sci

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“…In recent years, finite-source models in different forms have been effectively used, for example, for the mathematical description of a multiprogrammed computer system (see [4][5][6][7][8]). …”

Section: The Common Modelmentioning

confidence: 99%

Comparing two queueing models for nonhomogeneous nonreliable terminal systems

Almási

1995

J Math Sci

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This paper deals with two nonhomogeneous queueing models to describe the performance of finite multiterminal systems subject to random breakdowns. The difference between the two models is relatively small, but we will see that the differences between some system performance characteristics are very large(lO0~ or more). The other contribution of this paper is to introduce some new terminologies to queueing theory, which are necessary for the second model. All random variables involved here are independent and exponentially distributed. The models described here are generalizations of the homogeneous model treated earlier by different authors. At the end of this paper some numerical results illustrate the problem in question. The Common ModelThis paper deals with the analysis of a queueing system which may be used as a model of a real-life system consisting of n terminals connected with the Central Processor Unit (CPU). The user at the terminal i has exponentially distributed think times with rate A~ and generates jobs with the processing time being exponentially distributed with rate pi. The service rule at the CPU is First-In, First-Out (FIFO). Let us assume that the operational system is subject to random breakdowns stopping the service at the terminals and at the CPU. The failure-free operation times of the system are exponentially distributed random variables with rate a. The restoration times of the system are assumed to be exponentially distributed random variables with rate ~. The busy terminals are also subject to random breakdowns not affecting the system's operation. The failure-free operation times of busy terminals are assumed to be exponentially distributed random variables with rate 74 for the terminal i. The repair times of the terminal i are exponentially distributed random variables with rate 7"i. The breakdowns are serviced by a single repairman providing preemptive priority to the system's failure. We assume that each user generates only one job at a time, and he waits at the CPU before he starts thinking again, that is, the terminal is inactive while waiting at the CPU, and it cannot break down. All random variables involved here are independent of each other.As can easily be seen, this model is a generalization of the classical "machine interference problem" discussed among others, in [1][2][3]. In recent years, finite-source models in different forms have been effectively used, for example, for the mathematical description of a multiprogrammed computer system (see [4][5][6][7][8]). The First Mathematical ModelIn the first model we assume that the terminals are inactive while the system (CPU) is down; i.e., there is no job generation and there is no terminal failure.A detailed description and the calculation method of the steady-state probabilities of this model can be found in [4]. In what follows, we will use a simpler notation (than in

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“…An M/E k /1 queueing model with arrival rate dependent on server breakdown was investigated by Shogan [19]. Alam and Mani [1], Sztrik and Gál [20,21], Jayaraman et al [9], Wartenhorst [30], Hsieh and Andersland [7], Jain [8] studied the queueing models subject to random breakdowns. Further studies on this topic were done by Tang [27] and Ke [10].…”

Section: Introductionmentioning

confidence: 99%

M/E_k/1 Queueing System with Working Vacation

Jain

Agrawal

2007

Quality Technology & Quantitative Management

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__________________________________________________________________________Abstract: This paper deals with state dependent M/E k /1 queueing system with server breakdown and working vacation. As soon as the system becomes empty, the server leaves the system and takes vacation for random duration during which it may perform ancillary duty and is called on working vacation. It is assumed that the server may breakdown when it is busy. The vacation duration and the life time of server are exponentially distributed. Both service times in a working vacation and in a busy period are assumed to be Erlangian distributed. Once server starts the service, he continues until all jobs are served. The Chapman Kolmogorov equations are constructed in order to obtain the steady state probability distribution of the number of jobs in the system. The probability generating function is employed to obtain the average queue length and other system characteristics. Numerical experiment is performed to validate the analytical results. The sensitivity analysis has been done to examine the effect of different parameters.

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A recursive solution of a queueing model for a multi-terminal system subject to breakdowns

Cited by 23 publications

References 3 publications

The effects of service disciplines on the performance of a nonreliable terminal system

The effects of service disciplines on the performance of a nonreliable terminal system

Comparing two queueing models for nonhomogeneous nonreliable terminal systems

M/E_k/1 Queueing System with Working Vacation

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A recursive solution of a queueing model for a multi-terminal system subject to breakdowns

Cited by 23 publications

References 3 publications

The effects of service disciplines on the performance of a nonreliable terminal system

The effects of service disciplines on the performance of a nonreliable terminal system

Comparing two queueing models for nonhomogeneous nonreliable terminal systems

M/Ek/1 Queueing System with Working Vacation

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Product

Resources

About

M/E_k/1 Queueing System with Working Vacation