Simulation of IPA gradients in hybrid network systems

Infinitesimal Perturbation Analysis (IPA) provides formulas for derivatives (gradients) of performance measures with respect to parameters of interest, computed from sample paths of stochastic systems. In practice, IPA derivatives may be computed either from simulation runs or from empirical field data (when the formulas are non-parametric). Nonparametric IPA derivatives in fluid-flow queues have been recently derived for the loss volume and time average of buffer occupancy, with respect to buffer size, and arrival-rate or service-rate parameters. Additionally, these IPA derivatives have been shown to be unbiased in the sense that their expectation and differentiation operators commute, while their discrete counterparts have long been known to be generally biased. Recent work has further shown how to map the computation of IPA derivatives from a fluid-flow queue to its discrete counterpart without an appreciable loss of accuracy in performance measures. Thus, this work holds out the promise of potential applications of IPA derivatives to gradient-based optimization of objective functions involving performance metrics parameterized by settable parameters in queueing network context. This paper is an empirical study of IPA derivatives for individual queues within queueing systems which model telecommunications networks and some of their protocols. As a testbed, we used HNS (Hybrid Network Simulator) -a hybrid Java simulator of queueing networks with traffic streams subject to several telecommunications protocols. More specifically, the hybrid feature of HNS admits models with mixtures of discrete (packet) flows and continuous (fluid) flows, and collects detailed statistics and IPA derivatives for all flow types. The paper outlines the mapping of IPA derivatives from the fluid domain to the packet domain as implemented in HNS, and studies the accuracy of IPA derivatives in compatible fluid and packet queueing models, as well as the stabilization of their values in time. Our experimental results lend empirical support to the contention that IPA derivatives can be accurately computed from discrete versions by adopting a fluid-flow view. Furthermore, the long-run values IPA derivatives are empirically shown to stabilize quite fast. Finally, the results provide the basis and motivation for IPA applications to optimization of telecommunications network design and to potential new open-loop protocols that take advantage of IPA information.