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
Journal
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Language
English
Pages
330-341
Status
Published
DOI
10.1007/978-3-030-36614-8_25
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
Date of creation
10.02.2020
Date of change
10.02.2020
Short link
https://repository.rudn.ru/en/records/article/record/56423/
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