Queues and risk processes with dependencies

Research output: Contribution to journalArticleAcademicpeer-review

5 Citations (Scopus)
61 Downloads (Pure)

Abstract

We study the generalization of the G/G/1 queue obtained by relaxing the assumption of independence between inter-arrival times and service requirements. The analysis is carried out for the class of multivariate matrix exponential distributions introduced in Ref.[13]. In this setting, we obtain the steady-state waiting time distribution, and we show that the classical relation between the steady-state waiting time and workload distributions remains valid when the independence assumption is relaxed. We also prove duality results with the ruin functions in an ordinary and a delayed ruin process. These extend several known dualities between queueing and risk models in the independent case. Finally, we show that there exist stochastic order relations between the waiting times under various instances of correlation. Keywords: Dependence, Duality, G/G/1 queue, Insurance risk, Ruin probability, Stochastic ordering, Value at Risk, Waiting time, Workload
Original languageEnglish
Pages (from-to)390-419
Number of pages31
JournalStochastic Models
Volume30
Issue number3
DOIs
Publication statusPublished - 2014

Fingerprint Dive into the research topics of 'Queues and risk processes with dependencies'. Together they form a unique fingerprint.

  • Cite this