Jackson network in a random environment: strong approximation

2020/10/27 by Elena Bashtova, Bashtova, Elena, Elena Lenena +1
Business, Management and Accounting · Decision Sciences · #Advanced Queuing Theory Analysis #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Simulation Techniques and Applications

paper · pdf · doi:10.48550/arxiv.2010.14582

openalex publication_date 2020/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a Jackson network with regenerative input flows in which every server is subject to a random environment influence generating breakdowns and repairs. They occur in accordance with two independent sequences of i.i.d. random variables. We establish a theorem on the strong approximation of the vector of queue lengths by a reflected Brownian motion in positive orthant.

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