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ISyE's applied probability and simulation research spans from theoretical foundations to practical implementations. Current methodological studies in applied probability cover:
Approximation techniques for queuing network models.
Analysis of rare occurrences (such as large deviations, extreme values, and tail asymptotics) in queuing systems, Gaussian processes, and heavy-tailed scenarios.
Investigations of duality, mixing times, and phase transitions within controlled and uncontrolled Markov processes.
Development and evaluation of algorithms with associated combinatorial aspects.
Inventory management theory.
In simulation research, projects focus on enhancing the effectiveness and reliability of complex simulations. These initiatives include:
Refining simulation models through optimization techniques (like adaptive random search, ranking/selection methods, or multinomial selection).
Modeling stochastic processes with significant dependencies.
Sequential approaches for quantile estimation.
Variance reduction techniques for option pricing calculations.
Sampling methodologies from model manifolds.