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.

Авторы
Markovich N.1 , Razumchik R. 2, 3
Язык
Английский
Страницы
330-341
Статус
Опубликовано
Том
11965 LNCS
Год
2019
Организации
  • 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
Ключевые слова
Cluster and inter-cluster distributions; Cluster of exceedances; Extremal index; Lindley process; Queuing
Дата создания
10.02.2020
Дата изменения
10.02.2020
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/56423/
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