Per-flow structure of losses in a finite-buffer queue

• Published in: Applied mathematics and computation Vol. 428; p. 127215
• Main Author: Chydzinski, Andrzej
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.09.2022
• Subjects: Buffer overflows; Finite buffer; Loss characteristics; Multi-flow queue; Per-flow burst ratio; Routers; TCP/IP networks; Finite buffer; Loss characteristics; Routers; Buffer overflows; Multi-flow queue; TCP/IP networks; Per-flow burst ratio
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2022.127215

•The burst ratio can be derived separately for each flow in a queueing model with many flows of jobs arriving to a shared buffer, where they are subject to losses due to buffer overflows.•The per-flow burst ratios are usually not equal to each other and may differ by far, depending on flow rates or the number of flows.•The per-flow burst ratio decreases with the number of flows.•The per-flow burst ratio grows with the buffer size and the variance of the service time.•The per-flow burst ratio depends in a non-monotonic way on the system load. We analyze the structure of losses in individual flows, in a multi-flow, finite-buffer queueing system. Namely, a model with many separate flows (streams) of jobs arriving to a shared buffer, where they are subject to losses due to buffer overflows, is considered. (Such systems are common, for instance, in computer networking, where flows of packets arrive to the same router’s buffer from different network users). Assuming a general service time distribution and Poisson flows, we study the burst ratio parameter, which reflects the tendency of losses to cluster together, in long series. In particular, an explicit formula for the burst ratio in each individual flow is derived. Using this formula we show, among other things, that the per-flow burst ratio may vary significantly among flows and differ from the global burst ratio. This distinguishes the per-flow burst ratio from the per-flow loss ratio, which is the same for all flows. We demonstrate also the dependence of the per-flow burst ratio on the flow rate, number of flows, buffer size, system load and variance of the service time.