Research of Non-Markovian Queuing Networks
| Autor: | Nadezhda Bakhareva, Veniamin Tarasov |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
0209 industrial biotechnology
Queueing theory 021103 operations research Queue management system Computer science 0211 other engineering and technologies Probabilistic logic Markov process 02 engineering and technology Multiplexing symbols.namesake 020901 industrial engineering & automation Distribution (mathematics) Probability theory Flow (mathematics) symbols Applied mathematics |
| Zdroj: | 2018 International Scientific-Practical Conference Problems of Infocommunications. Science and Technology (PIC S&T). |
| DOI: | 10.1109/infocommst.2018.8632142 |
| Popis: | The article presents models of mathematical multiplexing and demultiplexing of flows, as well as the expressions for determining the numerical characteristics of the intervals distribution in the output flow from the queuing system (QS). Together they allow us to write the equations of equilibrium with respect to the mean values and variance in the time intervals distributions between neighboring states in queuing networks in case of random receiving flows patterns and service time. QS M${-}/M^{-}$/1 with a delay in time, $H_{2}/H _{2}$ /1 and H 2 /M/1 are considered to be the nodes of the network. With general assumptions about the probability of time distribution between neighboring states in the input flows and service time at the nodes, the proposed approach allows to determine average values and variances of time intervals between all the states of queuing network flows, as well as all the probabilistic properties of such networks. The approach can also be extended, if necessary, to third moments. From the perspective of probability theory, this will be more accurate than the calculation at the level of two moments of the distributions. Having incomplete information on the patterns of time intervals distribution, the proposed approach may be acceptable for the analysis of the performance of non-Markovian queuing networks. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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