Abstract
This chapter addresses \({M}^{X}/G/1/n\) queues, i.e., single server batch Markovian arrival queues with finite customer waiting space of size n. Taking profit of the Markov regenerative structure of these systems, we develop an efficient recursive procedure to compute the probability mass function of the number of losses in busy-periods starting with an arbitrary number of customers in the system. The derived computational procedure is easy to implement and leads to a fast numerical computation of the loss probabilities. To illustrate the effectiveness of the procedure, loss probabilities are computed for a wide variety of queues, with different capacities, batch size distributions, and arrival and service parameters.
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Acknowledgments
The authors thank the support of the Portuguese Government through FCT (Fundação para a Ciência e a Tecnologia) under the projects Pest-OE/MAT/UI0822/2011, PEst-OE/MAT/UI4080/2011, and PTDC/EIA-EIA/115988/2009.
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Ferreira, F., Pacheco, A., Ribeiro, H. (2013). Distribution of the Number of Losses in Busy-Periods of \({M}^{X}/G/1/n\) Systems. In: Lita da Silva, J., Caeiro, F., Natário, I., Braumann, C. (eds) Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications. Studies in Theoretical and Applied Statistics(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34904-1_17
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DOI: https://doi.org/10.1007/978-3-642-34904-1_17
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