期刊
STOCHASTIC MODELS
卷 30, 期 3, 页码 390-419出版社
TAYLOR & FRANCIS INC
DOI: 10.1080/15326349.2014.930603
关键词
Dependence; Duality; G/G/1 queue; Insurance risk; Ruin probability; Stochastic ordering; Value at Risk; Waiting time; Workload
资金
- Netherlands Organisation for Scientific Research (NWO) [613.001.017]
- IAP BESTCOM Project - Belgian goverment
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.
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