A queueing model for a non-homogeneous terminal system subject to BR992

Almási, B.; Sztrik, János

doi:10.1016/0898-1221(93)90253-r

Cited by 9 publications

(9 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If we know the steady-state probabilities, we can easily calculate some steady-state performance characteristics (see [3,4,6,9,10]). To compare the models with numerical results we will calculate the following steady-state characteristics.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…We can determine the steady-state probabilities using a recursive calculation method to reduce the effects of the round-off errors (see [4,5,9,10]). If we know the steady-state probabilities, we can easily calculate some steady-state performance characteristics (see [3,4,6,9,10]).…”

Section: Numerical Resultsmentioning

confidence: 99%

“…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 …”

Section: The First Mathematical Modelmentioning

confidence: 99%

“…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%

See 3 more Smart Citations

Comparing two queueing models for nonhomogeneous nonreliable terminal systems

Almási

1995

J Math Sci

View full text Add to dashboard Cite

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

show abstract

Section: Numerical Resultsmentioning

confidence: 99%

Section: Numerical Resultsmentioning

confidence: 99%

“…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 …”

Section: The First Mathematical Modelmentioning

confidence: 99%

Section: The Common Modelmentioning

confidence: 99%

See 2 more Smart Citations

Comparing two queueing models for nonhomogeneous nonreliable terminal systems

Almási

1995

J Math Sci

View full text Add to dashboard Cite

show abstract

“…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%