Abstract
We consider the MAP/PH/N queueing system with propagated breakdowns. Breakdowns arrive in bunches (we call them attacks) according to the MAP. The process of further arrival of different types of server failures within an attack is governed by phase type Markov process. Recovering of the server takes an exponentially distributed time with intensity depending on the type of the occurred failure. We describe the behavior of the system by the multi-dimensional continuous time Markov chain and analyze conditions for existence of its stationary behavior and compute its stationary distribution. Waiting time distribution and the key performance measures of the system are computed.
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Al-Begain, K., Dudin, A., Klimenok, V. (2010). Queueing System MAP/PH/N with Propagated Failures. In: Al-Begain, K., Fiems, D., Knottenbelt, W.J. (eds) Analytical and Stochastic Modeling Techniques and Applications. ASMTA 2010. Lecture Notes in Computer Science, vol 6148. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13568-2_2
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DOI: https://doi.org/10.1007/978-3-642-13568-2_2
Publisher Name: Springer, Berlin, Heidelberg
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