Avoidance versus detection and recovery problem in buffer-space allocation of flexibly automated production systems

Abstract

Motivated by recent developments in the semiconductor manufacturing industry, this paper undertakes an analytical investigation of the problem of selecting optimally the deadlock resolution strategy for buffer space allocation in flexibly automated production systems. In the process, it extends the behavioral models for the aforementioned systems currently considered in the literature, to account for probabilistic uncontrollable effects like the requirement for extra finishing steps and/or rework, and it introduces a new deadlock resolution scheme, characterized as randomized deadlock avoidance. The combination of these two extensions brings the considered system behavior(s) to the realm of probabilistic automata, an area of increasing academic interest. For the resulting model, and under the assumption of Markovian timings, it develops an analytical methodology for selecting the optimal deadlock resolution strategy that maximizes the steady-state system throughput, and it demonstrates its effectiveness through application to a "prototype" system configuration. The obtained results provide an interesting analytical expression of the need to assess the gains obtained by the increased concurrency supported by the deadlock detection and recovery strategy versus the productivity losses experienced under this approach due to increased system blocking, and/or additional material handling overheads. It turns out that, for the considered system configuration, the optimal selection scheme switches between detection and recovery and pure deadlock avoidance, every time that the time cost of deadlock recovery, tau(d), crosses a threshold Theta, which is a function of the remaining system behavioral and timing parameters. Beyond its own theoretical merit, this last result raises also the question of whether the policy randomization introduced in this work will ever enhance the performance of any configuration in the considered class of Resource Allocation Systems (RAS); this issue will be investigated in a sequel paper.