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September 2014 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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Adv. in Appl. Probab. 46(3): 812-831 (September 2014). DOI: 10.1239/aap/1409319561


We focus on a particular connection between queueing and risk models in a multidimensional 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 of 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.


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E. S. Badila. O. J. Boxma. J. A. C. Resing. E. M. M. Winands. "Queues and risk models with simultaneous arrivals." Adv. in Appl. Probab. 46 (3) 812 - 831, September 2014.


Published: September 2014
First available in Project Euclid: 29 August 2014

zbMATH: 1311.60103
MathSciNet: MR3254343
Digital Object Identifier: 10.1239/aap/1409319561

Primary: 60K25
Secondary: 91B30

Keywords: Duality , multivariate risk model , Queue with simultaneous arrival , stochastic decomposition , workload

Rights: Copyright © 2014 Applied Probability Trust


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Vol.46 • No. 3 • September 2014
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