Infinitesimal perturbation analysis of discrete event dynamic systems: A general theory

We give a rigorous extension of the perturbation analysis approach to more general Discrete Event Dynamic Systems (DEDS). For a fairly general class of DEDS, and for certain parameters and performance measures of such DEDS, an infinitesimal perturbation analysis algorithm is stated. It is then proved that this algorithm gives exact values for the gradients of performance w.r.t. the parameters, by observing only one sample-path of the DEDS. This enables very efficient calculation of these gradients: a fact that can be used for design/operation of manufacturing systems, communication networks, and many other real-world systems.

[1]  Frederick S. Hillier,et al.  Finite Queues in Series with Exponential or Erlang Service Times - A Numerical Approach , 1966, Oper. Res..

[2]  Michael A. Crane,et al.  Simulating Stable Stochastic Systems: III. Regenerative Processes and Discrete-Event Simulations , 1975, Oper. Res..

[3]  J. A. Buzacott.  The production capacity of job shops with limited storage space , 1976 .

[4]  K. Mani Chandy,et al.  Approximate Methods for Analyzing Queueing Network Models of Computing Systems , 1978, CSUR.

[5]  Peter J. Denning,et al.  The Operational Analysis of Queueing Network Models , 1978, CSUR.

[6]  Yu-Chi Ho,et al.  Parametric sensitivity of a statistical experiment , 1979 .

[7]  Yu-Chi Ho,et al.  A gradient technique for general buffer storage design in a production line , 1979 .

[8]  Philip Heidelberger,et al.  A spectral method for confidence interval generation and run length control in simulations , 1981, CACM.

[9]  Stephen S. Lavenberg,et al.  A Perspective on the Use of Control Variables to Increase the Efficiency of Monte Carlo Simulations , 1981 .

[10]  Christos G. Cassandras,et al.  Infinitesimal and finite perturbation analysis for queueing networks , 1982, 1982 21st IEEE Conference on Decision and Control.

[11]  Didier Dubois,et al.  Heuristic methods based on mean-value analysis for flexible manufacturing systems performance evaluation , 1982, 1982 21st IEEE Conference on Decision and Control.

[12]  Ernest Koenigsberg,et al.  Twenty Five Years of Cyclic Queues and Closed Queue Networks: A Review , 1982 .

[13]  Christos G. Cassandras,et al.  A new approach to the analysis of discrete event dynamic systems , 1983, Autom..

[14]  Xi-Ren Cao,et al.  Perturbation analysis and optimization of queueing networks , 1983 .

[15]  R. Suri.  Implementation of sensitivity calculations on a monte carlo experiment , 1983 .

[16]  Stanley B. Gershwin,et al.  Modeling and Analysis of Three-Stage Transfer Lines with Unreliable Machines and Finite Buffers , 1983, Oper. Res..

[17]  Y. Ho,et al.  Perturbation analysis of sojourn time in queueing networks , 1983, The 22nd IEEE Conference on Decision and Control.

[18]  Rajan Suri,et al.  Robustness of queuing network formulas , 1983, JACM.

[19]  Y. C. Ho,et al.  A New Approach to Determine Parameter Sensitivities of Transfer Lines , 1983 .