Reachability questions in piecewise deterministic Markov processes
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
Analysis of transient queues with semidefinite optimization
Queueing Systems: Theory and Applications
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We provide a new approach to the numerical computation of moments of the exit time distribution of Markov processes. The method relies on a linear programming formulation of a process exiting from a bounded domain. The LP formulation characterizes the evolution of the process through the moments of the induced occupation measure and naturally provides upper and lower bounds for the exact values of the moments. The conditions the moments have to satisfy are derived directly from the generator of the Markov process and are not based on some approximation of the process. Excellent software is readily available because the computations involve finite dimensional linear programs.