Mathematics and hybrid modeling: mathematics for simulation

ABSTRACT

I survey several mathematical techniques and results that are useful in the context of stochastic simulation. The concepts are introduced through the study of a simple model of ambulance operation to ensure clarity, concreteness and cohesion.

REFERENCES

• 1: Billingsley, P. 1986. Probability and measure. 2d ed. New York: Wiley.
• 2: Paul Bratley , Bennett L. Fox , Linus E. Schrage, A guide to simulation (2nd ed.), Springer-Verlag New York, Inc., New York, NY, 1987
• 3: Paul Glasserman, Filtered Monte Carlo, Mathematics of Operations Research, v.18 n.3, p.610-634, Aug. 1993 [doi>10.1287/moor.18.3.610]
• 4: Peter W. Glynn , Philip Heidelberger, Bias properties of budget constrained simulations, Operations Research, v.38 n.5, p.801-814, Sep./Oct. 1990 [doi>10.1287/opre.38.5.801]
• 5: P. W. Glynn , D. L. Iglehart, Simulation output analysis using standardized time series, Mathematics of Operations Research, v.15 n.1, p.1-16, Feb. 1990 [doi>10.1287/moor.15.1.1]
• 6: Peter W. Glynn, Some new results on the initial transient problem, Proceedings of the 27th conference on Winter simulation, p.165-170, December 03-06, 1995, Arlington, Virginia, United States [doi>10.1145/224401.224458]
• 7: Henderson, S. G. and P. W. Glynn. 1999. Computing densities for Markov chains via simulation. Submitted for publication.
• 8: Averill M. Law , David M. Kelton, Simulation Modeling and Analysis, McGraw-Hill Higher Education, 1999
• 9: Meyn, S. P. and R. L. Tweedie. 1993. Markov chains and stochastic stability. New York: Springer-Verlag.
• 10: Rice, J. A. 1988. Mathematical statistics and data analysis. Pacific Grove, California: Wadsworth and Brooks/Cole.
• 11: Serfling, R. J. 1980 Approximation theorems of mathematical statistics. New York: Wiley.