Abstract
We investigate clusters of extremes defined as subsequent exceedances of high thresholds in a Lindley process. The latter is usually used to model the waiting time or the length of a queue in queuing systems. Distributions of the cluster and inter-cluster sizes of the Lindley process are obtained for a given value of the threshold assuming that the process begins from the zero value. An example of a M/M/1 queue and the impact of service and arrival rates on the cluster and inter-cluster distributions are shown.
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CITATION STYLE
Markovich, N., & Razumchik, R. (2019). Cluster Modeling of Lindley Process with Application to Queuing. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11965 LNCS, pp. 330–341). Springer. https://doi.org/10.1007/978-3-030-36614-8_25
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