Abstract
This paper studies the tail of the buffer occupancy distribution of a queueing system with c parallel deterministic servers, infinite buffer capacity and an input process with consists of a superposition of a long range dependent on-off source and a batch renewal process. In particular, we investigate the decay of the tail for different values of c and for different compositions of the traffic mix. It is shown that for c = 1 (i.e. a single server system), the tail has a power law decay, while for c > 1, different cases may be distinguished: if the arrival rate of the background traffic is larger than c − 1, then the tail probabilities decay according to a power law, while for the other case, the decay is exponential.
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Daniëls, T., Blondia, C. (2000). Tail Transitions in Queues with Long Range Dependent Input. In: Pujolle, G., Perros, H., Fdida, S., Körner, U., Stavrakakis, I. (eds) Networking 2000 Broadband Communications, High Performance Networking, and Performance of Communication Networks. NETWORKING 2000. Lecture Notes in Computer Science, vol 1815. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45551-5_23
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DOI: https://doi.org/10.1007/3-540-45551-5_23
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