Abstract
During the past couple of years, a lot of effort has been put into solving all kinds of Markov Modulated discrete-time queueing models, which occur, almost in a natural way, in the performance analysis of slotted systems, such as ATM multiplexers and switching elements. However, in most cases, the practical application of such solutions is limited, due to the large state space that is usually involved. In this paper, we try to set a first step towards obtaining approximate solutions for a discrete-time multiserver queueing model with a general heterogeneous Markov Modulated cell arrival process, that allow accurate predictions concerning the behavior of the buffer occupancy in such a model, and still remains tractable, both from an analytical and a computational point-of-view. We first introduce a solution technique which leads to a closed-form expression for the joint probability generating function of the buffer occupancy and the state of the arrival process, from which an expression for V(z), the probability generating function of the buffer occupancy is easily derived. Based on this result, for the single-server case, we propose an approximation for the boundary probabilities, that reduces all calculations to an absolute minimum. In addition, we show how accurate data for the distribution of the buffer occupancy can be obtained, by using multiple poles of V(z) in the geometric-tail approximation of the distribution.
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© 1996 Springer Science+Business Media Dordrecht
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Steyaert, B., Xiong, Y. (1996). Buffer requirements in ATM-related queueing models with bursty traffic: an alternative approach. In: Fdida, S., Onvural, R.O. (eds) Data Communications and their Performance. IFIP — The International Federation for Information Processing. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-34942-8_11
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DOI: https://doi.org/10.1007/978-0-387-34942-8_11
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