2025/06/29 by Sergey Foss, Foss, Sergey, Masakiyo Miyazawa +3
Business, Management and Accounting · Decision Sciences · Engineering · #60F10 #60K20 #60K25 #Advanced Queuing Theory Analysis #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Reliability and Maintenance Optimization
paper · pdf · doi:10.48550/arxiv.2506.23310
openalex publication_date 2025/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a Generalised Jackson Network with finitely many servers, a renewal input and i.i.d. service times at each queue. We assume the network to be stable and, in addition, the distribution of the inter-arrival times to have unbounded support. This implies that the length of a typical busy period B, which is the time between two successive idle periods, is finite a.s. and has a finite mean. We assume that the distributions of the service times with the heaviest tails belong to the class of so-called intermediate regularly varying distributions. We obtain the exact asymptotics for the probability \mathbb P (B>x), as x→∞. For that, we show that the Principle of a Single Big Jump holds: B takes a large value mainly due to a single unusually large service time.