Perturbation Analysis of Discrete Event Dynamical Systems with Applications to Manufacturing

The perturbation analysis approach has been proved to be very useful in analyzing and optimizing the discrete event dynamic systems (DEDS). The approach derives the exact value of the sensitivities of the system performance with respect to system parameters, by only observing one sample experiment of the system. Comparing with the conventional approach for optimizing DEDS performance, the analytic method and the simulation method. this approach has many advantages. It avoids the numerical problems associated with computing a finite difference of noisy functions. It does not suffer from the constraining assumptions required by the analytic models, i.e., it applies to most general DEDS almost without any restrictions. Besides, it obtains the sensitivities with respect to all parameters from one experiment, hence saves many simulation runs. This new approach to DEDS analysis was introduced by Ho et. al. [1] to solve a design problem in production lines. Extensions and formalizations to determine throughput sensitivity (gradient) with respect to various parameters for tandem queues were given in [2-8]. The method was generalized for throughput sensitivity w.r.t service time parameters, in queueing networks at equilibrium [7-8]. The sensitivity analysis of performance w.r.t finite changes in parameters was discussed in [9]. Determination of throughput sensitivity w.r.t number of customers in a multiclass closed network enabled application to flexible manufacturing [10] and computer communication systems [11]. Sensitivity of a new performance measure, sojourn time in queueing networks was studied w.r.t service time parameters in [12]. Some related modelling issues were formally analyzed in [13-15].