2009/09/03 by Amr Rizk, Rizk, Amr, Markus Fidler +1
Business, Management and Accounting · Computer Science · Engineering · #Advanced Queuing Theory Analysis #Advanced Wireless Network Optimization #FOS: Computer and information sciences #Network Traffic and Congestion Control #Networking and Internet Architecture (cs.NI) #Performance (cs.PF) #cs.NI #cs.PF
paper · pdf · doi:10.48550/arxiv.0909.0633
arxiv created 2009/09/03 · openalex publication_date 2009/09/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Fractional Brownian motion (fBm) emerged as a useful model for self-similar and long-range dependent Internet traffic. Approximate performance measures are known from large deviations theory for single queuing systems with fBm through traffic. In this paper we derive end-to-end performance bounds for a through flow in a network of tandem queues under fBm cross traffic. To this end, we prove a rigorous sample path envelope for fBm that complements previous approximate results. We find that both approaches agree in their outcome that overflow probabilities for fBm traffic have a Weibullian tail. We employ the sample path envelope and the concept of leftover service curves to model the remaining service after scheduling fBm cross traffic at a system. Using composition results for tandem systems from the stochastic network calculus we derive end-to-end statistical performance bounds for individual flows in networks under fBm cross traffic. We discover that these bounds grow in O(n (log n)^(1/(2-2H))) for n systems in series where H is the Hurst parameter of the fBm cross traffic. We show numerical results on the impact of the variability and the correlation of fBm traffic on network performance.