Synchronized Lévy queues. (December 2020)

• Record Type: Journal Article
• Authors: Kella, Offer; Boxma, Onno
• Is Part Of: Journal of applied probability. Volume 57:Number 4(2020)
• Page Start: 1222
• Page End: 1233
• Publication Date: 2020-12
• Subjects: Lévy driven queues, -- synchronized Lévy queues, -- decomposition; 60G51, -- 60K25, -- 90B05; 519.2
• DOI: 10.1017/jpr.2020.75
• Languages: English
• ISSNs: 0021-9002

Abstract

Abstract: We consider a multivariate Lévy process where the first coordinate is a Lévy process with no negative jumps which is not a subordinator and the others are non-decreasing. We determine the Laplace–Stieltjes transform of the steady-state buffer content vector of an associated system of parallel queues. The special structure of this transform allows us to rewrite it as a product of joint Laplace–Stieltjes transforms. We are thus able to interpret the buffer content vector as a sum of independent random vectors.