Queues and risk models with simultaneous arrivals

E.S. Badila, O.J. Boxma, J.A.C. Resing, E.M.M. Winands

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Samenvatting

We focus on a particular connection between queueing and risk models in a multi-dimensional setting. We first consider the joint workload process in a queueing model with parallel queues and simultaneous arrivals at the queues. For the case that the service times are ordered (from largest in the first queue to smallest in the last queue) we obtain the Laplace-Stieltjes transform of the joint stationary workload distribution. Using a multivariate duality argument between queueing and risk models, this also gives the Laplace transform of the survival probability of all books in a multivariate risk model with simultaneous claim arrivals and the same ordering between claim sizes. Other features of the paper include a stochastic decomposition result for the workload vector, and an outline how the two-dimensional risk model with a general two-dimensional claim size distribution (hence without ordering of claim sizes) is related to a known Riemann boundary value problem.
Originele taal-2Engels
Plaats van productieEindhoven
UitgeverijEurandom
Aantal pagina's24
StatusGepubliceerd - 2012

Publicatie series

NaamReport Eurandom
Volume2012018
ISSN van geprinte versie1389-2355

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Citeer dit

Badila, E. S., Boxma, O. J., Resing, J. A. C., & Winands, E. M. M. (2012). Queues and risk models with simultaneous arrivals. (Report Eurandom; Vol. 2012018). Eindhoven: Eurandom.