Abstract
This paper investigates a queuing system with infinite number of servers where the arrival process is given by a Markov Arrival Process (MAP) and the service time follows a Phase-type (PH) distribution. They were chosen since they are simple enough to describe the model by exact methods. Moreover, highly correlated arrival processes and heavy-tailed service time distributions can be approximated by these tools on a wide range of time-scales. The transient behaviour of the system is analysed and the time-dependent moments of the queue length is computed explicitly by solving a set of differential equations. The results can be applied to models where performance of parallel processing is important. The applicability of the model is illustrated by dimensioning a WEB-based content provider.
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Vaderna, P., Éltető, T. (2006). Transient Analysis of a Queuing System with Matrix-Geometric Methods. In: Koucheryavy, Y., Harju, J., Iversen, V.B. (eds) Next Generation Teletraffic and Wired/Wireless Advanced Networking. NEW2AN 2006. Lecture Notes in Computer Science, vol 4003. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11759355_5
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DOI: https://doi.org/10.1007/11759355_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34429-2
Online ISBN: 978-3-540-34430-8
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