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DESCRIPTION:Title: Lévy driven queues: the workload correlation function is
  positive\, decreasing and convex\n\nAbstract:In this talk I will consider
  Lévy-driven queues\, i.e.\, reflected Lévy processes\, with a focus on st
 ructural properties of the workload correlation function. After having int
 roduced the objects studied\, I'll proceed by stating the conjecture that 
 has been around for quite a while\, namely that the workload correlation i
 s a positive\, decreasing and convex function of time. As a historic accou
 nt\, I'll briefly discuss the seminal contribution by Ott on the special c
 ase of the M/G/1 queue\, based on exploiting properties of complete monoto
 ne functions. The same methodology has been used in the extension (by Es-S
 aghouani and me) to queues with spectrally positive Lévy input\, whereas l
 ater (in a paper by Glynn and me) the spectrally negative case was dealt w
 ith. For a long time\, there was little hope to prove the conjecture for g
 eneral Lévy input (and\, for that matter\, for reflected random walks in d
 iscrete-time). In a recent paper (that I wrote with Berkelmans and Cichock
 a)\, we provide an elementary proof\, only relying on basic properties of 
 Lévy processes and their reflected version. Importantly\, the argumentatio
 n extends to double reflection\, and also covers reflected random walks. T
 ime permitting\, I also discuss various ramifications due to Kella and me\
 , and I comment on the question whether the structural properties carry ov
 er to the Markov modulated case.\n\n\n	Zoom link: https://mcgill.zoom.us/j/
 81120610248?pwd=Dt7gaqRsywfBL6oa5ou46WaqUeUf6s.1\n	\n	 \n
DTSTART:20250123T163000Z
DTEND:20250123T173000Z
LOCATION:Room 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:Michel Mandjes (Leiden)
URL:/mathstat/channels/event/michel-mandjes-leiden-362
 737
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