The Analysis of Queuing System with General Service Distribution and Renovation
| Autor: | E. V. Bogdanova, I. S. Zaryadov, Tatiana Milovanova |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Service (business)
Mathematical optimization Queue management system Markov chain Distribution (number theory) Computer science media_common.quotation_subject Real-time computing Poisson distribution symbols.namesake Task (computing) Order (business) symbols General Earth and Planetary Sciences Function (engineering) General Environmental Science media_common |
| Zdroj: | RUDN JOURNAL OF MATHEMATICS, INFORMATION SCIENCES AND PHYSICS. 25:3-8 |
| ISSN: | 2312-9743 2312-9735 |
| DOI: | 10.22363/2312-9735-2017-25-1-3-8 |
| Popis: | We investigate the queueing system in which the losses of incoming orders due to the introduction of a special renovation mechanism are possible. The introduced queueing system consists of server with a general distribution of service time and a buffer of unlimited capacity. The incoming flow of tasks is a Poisson one. The renovation mechanism is that at the end of its service the task on the server may with some probability empty the buffer and leave the system, or with an additional probability may just leave the system. In order to study the characteristics of the system the Markov chain embedded upon the end of service times is introduced. Under the assumption of the existence of a stationary regime for the embedded Markov chain the formula for the probability generation function is obtained. With the help of the probability generation function such system characteristics as the probability of the system being empty, the average number of customers in the system, the probability of a task not to be dropped, the distribution of the service waiting time for non-dropped tasks, the average service waiting time for non-dropped requests are derived. |
| Databáze: | OpenAIRE |
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