Institute for Systems Research

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Author: search.filters.author.Marcus, Steven I.Subject: search.filters.subject.flexible manufacturing

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    Randomized Difference Two-Timescale Simultaneous Perturbation Stochastic Approximation Algorithms for Simulation Optimization of Hidden Markov Models
    (2000) Bhatnagar, Shalabh; Fu, Michael C.; Marcus, Steven I.; Bhatnagar, Shashank; Marcus, Steven I.; Fu, Michael C.; ISR
    We proposetwo finite difference two-timescale simultaneous perturbationstochastic approximation (SPSA)algorithmsfor simulation optimization ofhidden Markov models. Stability and convergence of both thealgorithms is proved.

    Numericalexperiments on a queueing model with high-dimensional parameter vectorsdemonstrate orders of magnitude faster convergence using thesealgorithms over related $(N+1)$-Simulation finite difference analoguesand another two-simulation finite difference algorithm that updates incycles.

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    Optimal Multilevel Feedback Policies for ABR Flow Control using Two Timescale SPSA
    (1999) Bhatnagar, Shalabh; Fu, Michael C.; Marcus, Steven I.; ISR
    Optimal multilevel control policies for rate based flow control in available bit rate (ABR) service in asynchronous transfer mode (ATM) networks are obtained in the presence of information and propagation delays, using a numerically efficient two timescale simultaneous perturbation stochastic approximation (SPSA) algorithm. Numerical experiments demonstrate fast convergence even in the presence of significant delays and a large number of parametrized parameter levels.
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    Finite Buffer Realization of Input-Output Discrete Event Systems
    (1994) Kumar, Ratnesh; Garg, Vijay K.; Marcus, Steven I.; ISR
    Many discrete event systems (DESs) such as manufacturing systems, data base management systems, communication networks, traffic systems, etc., can be modeled as input-output discrete event systems (I/O DESs). In this paper we formulate and study the problem of stable realization of such systems in the logical setting. Given an input and an output language describing the sequences of events that occur at the input and the output, respectively, of an I/O DES, we study whether it is possible to realize the system as a unit consisting of a given set of buffers of finite capacity, called a dispatching unit. The notions of stable, conditionally stable, dispatchable and conditionally dispatchable units are introduced as existence of stable (or input-output bounded), and causal (or prefix preserving) input- output maps, and effectively computable necessary and sufficient conditions for testing them are obtained.
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    Ergodic Control of Switching Diffusions
    (1992) Ghosh, Mrinal K.; Arapostathis, Aristotle; Marcus, Steven I.; ISR
    We study the ergodic control problem of switching diffusions representing a typical hybrid system that arises in numerous applications such as fault tolerant control systems, flexible manufacturing systems, etc. Under certain conditions, we establish the existence of a stable Markov nonrandomized policy which is almost surely optimal for a pathwise longrun average cost criterion. We then study the corresponding Hamilton-Jacobi- Bellman (HJB) equation and establish the existence of a unique solution in a certain class. Using this, we characterize the optimal policy as a minimizing selector of the Hamiltonian associated with the HJB equations. We apply these results to a failure prone manufacturing system and show that the optimal production rate is of the hedging point type.
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    Optimal Control of Switching Diffusions with Application to Flexible Manufacturing Systems
    (1991) Ghosh, Mrinal K.; Arapostathis, Aristotle; Marcus, Steven I.; ISR
    A Controlled switching diffusion model is developed to study the hierarchical control of flexible manufacturing systems. The existence of a homogeneous Markov nonrandomized optimal policy is established by a convex analytic method. Using the existence of such a policy, the existence of a unique solution in a certain class to the associated Hamilton-Jacobi-Bellman equations is established and the optimal policy is characterized as a minimizing selector of an appropriate Hamiltonian.