On the optimality of randomized deadlock avoidance policies

Revisits the problem of the optimality of randomized deadlock avoidance policies for sequential resource allocation systems. The undertaken problem assumes that the various timing distributions are exponential and the performance objective of interest is the maximization of the system throughput. Our main finding is that under the aforestated assumptions, the randomization of the deadlock resolution policy does not lead to any efficiency increases. In other words, there will always exist an optimal solution in which each of the critical transitions from the safe to the unsafe region will always remain enabled or disabled. It is also shown, however, that randomization of the control of (some of) these transitions can provide an effective mechanism for accommodating additional operational constraints, like the observation of certain production ratios. Finally, an additional outcome of the presented work is the explicit characterization of the functional dependence of the considered objective function(s) to the system transition rates and the associated control variables, which provides broader insights regarding the (performance) control of continuous-time Markov chains under steady-state operation.