Discrete event systems with stochastic processing times

Discrete event dynamic systems are studied in which the underlying algebra is the max-algebra and the coefficients in the system, referring to processing times in practice, are stochastic. The processing times and/or the transportation times within a network show stochastic fluctuations. The restrictions are that the stochastic processing times of the nodes in the network are independent and identically distributed. The asymptotic behavior of the system is investigated, and the average duration of one cycle of the process is calculated. A specific example of the theory is considered. The state space is two-dimensional, and the probability distributions are exponential. It is shown that the process approaches a stationary limit as time proceeds. The case when the probability distributions are discrete is also treated. Several examples are given. Two-dimensional systems and, more generally, finite-dimensional systems are considered