IPA for continuous stochastic marked graphs

This paper presents a unified framework for the Infinitesimal Perturbation Analysis (IPA) gradientestimation technique in the setting of marked graphs. It proposes a systematic approach for computing the derivatives of sample performance functions with respect to structural and control parameters. The resulting algorithms are recursive in both time and network flows, and their successive steps are computed in response to the occurrence and propagation of certain events in the network. Such events correspond to discontinuities in the network flow-rates, and their special characteristics are due to the properties of continuous transitions and fluid places. Following a general outline of the framework we focus on a simple yet canonical example, and investigate throughput and workloadrelated performance criteria as functions of structural and control variables. Simulation experiments support the analysis and testify to the potential viability of the proposed approach. Published as: Y. Wardi, A. Giua, C. Seatzu, “IPA for Continuous Stochastic Marked Graphs,” Automatica, Vol. 49, No. 5, pp. 1204-1215, May, 2013. DOI: 10.1016/j.automatica.2013.02.006. ∗This work has been partially supported by the European Community’s Seventh Framework Programme under project DISC (Grant Agreement n. INFSO-ICT-224498). †Yorai Wardi (corresponding author, email: [email protected]) is with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia, USA. Alessandro Giua (email: [email protected]) is with DIEE, University of Cagliari, Italy and with LSIS, University of Aix-Marseille, France. Carla Seatzu (email: [email protected]) is with DIEE, University of Cagliari, Italy.