Properties and performance modelling of finite buffer \(M/G/1/K\) networks.

*(English)*Zbl 1202.90090Summary: Finite buffer, single-server queueing systems and networks are difficult to analyze since the length of time a customer spends in the system does not follow the Markovian property. A two-moment approximation schema is developed for the probability distribution of \(M/G/1/K\) systems and extended to the analysis of \(M/G/1/K\) queueing networks. The general purpose of this paper is to develop a flexible and practical transform-free approach for computing the probability distribution and performance measures of the system as well as identify the underlying properties of these systems. It is shown that for most performance measures, a sigmoid or S-shaped curve with an inflection point at \(\rho =1\) appears as \(K\rightarrow \infty \). This has direct implications for the analysis and optimization of such systems. The performance modelling of the \(M/G/1/K\) queueing networks of general topologies along with extensive numerical results accompany the paper along with the linear concave performance measures for these systems.

##### MSC:

90B22 | Queues and service in operations research |

90B15 | Stochastic network models in operations research |

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\textit{J. M. Smith}, Comput. Oper. Res. 38, No. 4, 740--754 (2011; Zbl 1202.90090)

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