A scaled stochastic approximation algorithm

Article Abstract:

A scaled stochastic approximation algorithm for determining the root of the gradient of the response function of complex stochastic systems is introduced. The new procedure, which optimizes stochastic systems in terms of several continuous input parameters or decision variables, eliminates the difficulties associated with the classical algorithm when applied to flat and steep functions. Specifically, it is not dependent on the steepness of the underlying functions, it converges faster, and it converges on a more general class of objective functions. It involves the sampling of two independent gradient estimates of the optimal input-parameter vector to derive a 'scale-free estimate of the next direction.' A comparison of the new algorithm with the Robbins-Monro algorithm in the context of two queueing systems demonstrates its advantages.

Algorithms, Stochastic systems, Stochastic approximation, Parameter estimation

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Pricing and capacity decisions for a service facility: stability and multiple local optima

Article Abstract:

A model of optimal pricing and capacity for a single-server queuing system in a service-based business is proposed. Difficulty is encountered in determining an optimal solution in the interior of the feasible region. This indicates the possibility that the proposed model does not characterize differential conditions of the first order. Stable arrival rates at equilibrium are achieved only when service rates are at values over the threshold. These rates are observed to be influenced by the admission rates and the service value parameters for uniform distribution. Thus, the M/M/one queue was used to demonstrate the stability of equilibrium service value to customers and to show the convergence of an algorithm with dynamic and adaptive features in determining arrival and service rates that are optimal.

Management, Pricing, Industrial capacity

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A two-moment approximation for the mean waiting time in the 'GI-G-s' queue

Article Abstract:

A simple two-moment approximation formula is presented for the mean waiting time in a 'GI-G-s' queue. The formula is in the form of a specific combination of the exact mean waiting times for the 'D-M-s', 'M-D-s' and 'M-M-s' queues, which means it can be calculated simply by known solutions in specific cases.

Models, Analysis, Scheduling (Management), Mathematical models, Approximation theory, Approximation

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