Abstract
This paper considers a stable GI∨GI∨1 queue with a regularly varying service time distribution. We derive the tail behaviour of the integral of the queue length process Q(t) over one busy period. We show that the occurrence of a large integral is related to the occurrence of a large maximum of the queueing process over the busy period and we exploit asymptotic results for this variable. We also prove a central limit theorem for ∫0t Q(s) ds.
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AMS subject classification: 60K25, 90B22.
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Kulik, R., Palmowski, Z. Tail Behaviour of the Area Under the Queue Length Process of the Single Server Queue with Regularly Varying Service Times. Queueing Syst 50, 299–323 (2005). https://doi.org/10.1007/s11134-005-0926-2
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DOI: https://doi.org/10.1007/s11134-005-0926-2