Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 11965 LNCS. 2019. P.. 165-178
Cluster Modeling of Lindley Process with Application to Queuing
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. © Springer Nature Switzerland AG 2019.
Authors
Markovich N. 1 , Razumchik R. 2, 3
Language
English
Pages
330-341
State
Published
Volume
11965 LNCS
Year
2019
Organizations
- 1 V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Profsoyuznaya Street 65, Moscow, 117997, Russian Federation
- 2 Institute of Informatics Problems, FRC CSC RAS, Vavilova Street 44-2, Moscow, 119333, Russian Federation
- 3 Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, Moscow, 117198, Russian Federation
Keywords
Cluster and inter-cluster distributions; Cluster of exceedances; Extremal index; Lindley process; Queuing
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Other records
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 11965 LNCS. 2019. P.. 469-478