Throughput in stochastic free-choice nets under various policies

In this paper, live and bounded free-choice Petri nets with stochastic firing times are considered. Several classical routing policies, namely the race policy, Bernoulli routings, and periodic routings, are compared in terms of the throughputs of the transitions. First, under general i.i.d. assumptions on the firing times, the existence of the throughput for the three policies is established. We also show that the ratio between the throughputs of two transitions depend only on the asymptotic frequencies of the routings, and not on the routing policy. On the other hand, the total throughput depends on the policy, and is higher for the race policy than for Bernoulli routings. Second, we show how to compute the throughput for exponentially distributed free-choice nets under the three policies. This is done by using Markov processes over appropriate state spaces. We use this to compare the performance of periodic and Bernoulli routings. Finally, we derive optimal policies under several information structures, namely, the optimal pre-allocation, the optimal allocation, and the optimal non-anticipative policy.