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The importance of the order two Markovian arrival process (MAP(2)) comes from its compactness, serving either as arrival or service process in applications, and from the nice properties which are not available for higher order MAPs. E.g., for order two processes the acyclic MAP(2) (AMAP(2)), the MAP(2) and the order two matrix exponential process (MEP(2)) are equivalent. Additionally, MAP(2) processes...
In contemporary control nets, random access schemes like CSMA are commonly used and are often enhanced by fixed priorities for some message types to guarantee an upper bound for the transmission time of high-priority messages. The introduction of priorities has a significant impact on the overall quality of service, which means that messages with a low priority may have long transmission times or...
Markov models are useful in the performance and dependability assessment of systems to obtain quantitative information that helps in making design decisions. The many known analysis techniques can be partitioned into approximate and exact techniques, where the former can be usually applied with limited effort but unknown precision and the latter give exact results but for the price of a computationally...
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