On per-flow delay bounds in tandem queues under (In)dependent arrivals

Abstract

Tandem queues, i.e., several servers in series, occur in many performance models of networked and distributed systems. In this paper, we derive stochastic delay bounds for a flow of interest from a set of flows that traverses the tandem. To that end, we take an approach based on stochastic network calculus (SNC) using moment-generating functions. Directly applying existing SNC approaches from literature requires to take into account many stochastic dependencies unless we incorporate the pay multiplexing only once (PMOO) principle known from deterministic network calculus (DNC). We derive a general solution for the tandem of n servers. Moreover, we also enable the analysis of stochastic dependencies among flows. In numerical experiments with fractional Brownian motion as a traffic model, we compare the delay bounds obtained by our analysis, following the PMOO principle, with those from existing literature and observe an average improvement of the delay bounds by at least 30%. Furthermore, we observe that by careful parameter optimization, a significant improvement is achieved compared to standard choices for the parameter set. Finally, we evaluate the effect of stochastic dependencies among flows on the delay bounds.