Abstract
In this study astochastic service system which has single-channel with exponential service time, recurrent input and finite queue, was investigated.
Laplace-Stieltjes transformation of times between loss moments of customer and loss probability of customer were obtained by using semi-Markov process method. In addition, it was showed that under quick service condition the stream of overflows convergenes to the Poisson stream.
Keywords
Interarrival Time Service Time Stream of Overflows Semi-Markov Process Laplace-Stieltjes Transformation Loss Probability
References
- AKULINICHEV, N.M. and Groskiy, Limiting distribution of additive functionals in certain queueing problems, Izv. Akad. Nauk SSSR, Technical Kibern., 1971, 1, 44-51 (Russian).
- BELYAYEV, Y.K. Limiting theorems for overflow streams, Theory Probability and Appl., 1963, 8, 175-194 (in Russian).
- ÇINLAR, E. Introduction to stochastic processes, Englewood Cliffs., 1970, New York.
- ÇINLAR, E., Disney, R.L. Stream of overflows from a finite queue, Oper. Res., 1967, 15, 131-134.
- KLIMOV, ɼ. P. Stochastic servers systems., 1966, Moscow.
- PALM, C. Intensitatschwwankungen fernsperchverkehr, Ericsson and Technics., 1943, 44, 1-189.
- PYKE, R. Markov renewal processes with finitely many states, Ann. Math. Stat., 1961, 32, 1243-1259.
- POURBABAİ, B. Approximation of the overflow process from a G/M/N/K queueing system, Management Science., 11987, 33, 931-937.
- SHAHBAZOV A.A. On the stream of losses from a finite queue, Technical Kibern., 1986, 6, 105-110 (in Russian).
- TAKACS, L. On generalisation Erlang’s formula, Ann. Math. Stat. 1969, 40, 71-78.
- TAKACS, L. Introduction to the theory of queues, Oxford University Press, New York, 1962.
- VINOGRADOV, O.P. Limiting distribution for first time of lost customer ın queue with limited waiting room, Math. Notes., 1968, 3, 541-546 (in Russian).
Abstract
Bu çalışmada sonlu kuyruklu, rekurent girişli ve çalışma süresi üstel dağılıma uyan tek kanallı bir stokastik hizmet sistemi araştırılmıştır. Yarı Markov süreçleri yöntemiyle sistemde müşterilerin kaybolma anları arasındaki sürelerin LS dönüşümü ve müşterinin kaybolma olasılığı bulunmuştur. Ayrıca “hızlı hizmet” koşulu altında kaybolan müşteri akımının Poisson akımına yaklaştığı açıklanmıştır.
Keywords
Gelişlerarası Süre Hizmet Süresi Kaybolan Müşteri Akımı Yarı Markov Süreci Laplace-Stieltjes Dönüşümü Kaybolma Olasılığı
References
- AKULINICHEV, N.M. and Groskiy, Limiting distribution of additive functionals in certain queueing problems, Izv. Akad. Nauk SSSR, Technical Kibern., 1971, 1, 44-51 (Russian).
- BELYAYEV, Y.K. Limiting theorems for overflow streams, Theory Probability and Appl., 1963, 8, 175-194 (in Russian).
- ÇINLAR, E. Introduction to stochastic processes, Englewood Cliffs., 1970, New York.
- ÇINLAR, E., Disney, R.L. Stream of overflows from a finite queue, Oper. Res., 1967, 15, 131-134.
- KLIMOV, ɼ. P. Stochastic servers systems., 1966, Moscow.
- PALM, C. Intensitatschwwankungen fernsperchverkehr, Ericsson and Technics., 1943, 44, 1-189.
- PYKE, R. Markov renewal processes with finitely many states, Ann. Math. Stat., 1961, 32, 1243-1259.
- POURBABAİ, B. Approximation of the overflow process from a G/M/N/K queueing system, Management Science., 11987, 33, 931-937.
- SHAHBAZOV A.A. On the stream of losses from a finite queue, Technical Kibern., 1986, 6, 105-110 (in Russian).
- TAKACS, L. On generalisation Erlang’s formula, Ann. Math. Stat. 1969, 40, 71-78.
- TAKACS, L. Introduction to the theory of queues, Oxford University Press, New York, 1962.
- VINOGRADOV, O.P. Limiting distribution for first time of lost customer ın queue with limited waiting room, Math. Notes., 1968, 3, 541-546 (in Russian).
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Statistical Theory |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | August 16, 2002 |
| Published in Issue | Year 2002 Volume: 1 Issue: 2 |
