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- W2248279518 abstract "Numerous studies demonstrate that correlation in the arrival process might have a significant influence on the behaviour of queueing systems. The impact of correlation on batch-service queueing systems, nevertheless, has attracted nearly no attention, and therefore constitutes the subject of this contribution. More specifically, we deduce various performance measures related to the buffer content in a system whereby the batch server only initiates service if the buffer content reaches or exceeds some server threshold. Such a threshold leads to a better utilization of the server capacity. We further include a general dependency between the service time of a batch and the number of customers within it. In addition, we model the correlation by a discrete batch Markovian arrival process (D-BMAP), i.e. the distribution of the number of customer arrivals per slot depends on a background state which is determined by a first-order Markov chain. This process is the subject of many papers, as it has the advantage that it can capture most arrival patterns up to any desired precision. By means of the obtained performance measures, we examine the influence of correlation on the behaviour of the system. For instance, we demonstrate that disregarding correlation, although it might lead to a severe underestimation of the buffer content, has only a small influence on the value of the optimal server threshold." @default.
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- W2248279518 date "2010-01-01" @default.
- W2248279518 modified "2023-09-27" @default.
- W2248279518 title "Influence of correlation in the arrival process on batch-service queueing systems" @default.
- W2248279518 hasPublicationYear "2010" @default.
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