SUBADDITIVITY AND STABILITY OF A CLASS OF DISCRETE-EVENT SYSTEMS

We investigate the stability of discrete-event systems modeled as gene ralized semi-Markov processes with event epochs that satisfy (max, +) recursions. We obtain three types of results, under conditions: We sho w that there exists for each event a cycle time, which is the long-run average time between event occurrences; we characterize the rate of c onvergence to this limit, bounding the error for finite horizons; and we give conditions for delays (i.e., differences between event epochs) to converge to a stationary regime, The main tools for the cycle time results are (max, +) matrix products and the subadditive ergodic theo rem. The convergence rate result (which assumes bounded i.i.d. inputs) is based on a martingale inequality. The stability of delays is deriv ed from existing results on the stability of stochastic difference equ ations. We discuss connections with these different fields, with the g eneral theory of random matrix products and with recent results for di screte-event systems.