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Research

Traffic

Our lab's primary research interest is in applied probability and stochastic processes, game theory and control and statistical modeling, with a focus on the stochastic modeling of service, communication and computing systems. Our current work includes:

  • Transitory Queueing Theory: queueing theory focuses largely on large time-scale phenomena. Here, we study small time-scale behavior of queueing models, and develop rigorously justified approximations to the performance of the models (with Rahul Jain and Amy Ward).

  • Traffic Models: a common modeling assumption in queueing theory is that job arrivals can be modeled (reasonably) accurately by Poisson, or renewal, processes. This is typically a sub-optimal assumption. We study alternative models that emerge as a consequence of games played between users submitting jobs, or as a consequence of an external control mechanism (with Rahul Jain, Mor Armony and Rami Atar).

  • Emergence of Non-Poisson Behavior: queueing theory is really the study of stochastic models at different time-scales. Another line of work studies the fact that observed trace data in call centers and hospitals display strong correlative effects at time-scales much longer ('macroscopic’ or 'mesoscopic’) than individual inter-arrival times ('microscopic’) by leveraging statistical modeling and the Palm-Khintchine Theorem (with Peter Glynn).

  • Approximations to non-stationary Markov processes: we develop analytical and numerical approximations to the conditional expectation of functions of the Markov process (ongoing with Peter Glynn).

  • Healthcare Systems Modeling: we developed stochastic models of operating room schedules in elective surgery hospitals (with Naumaan Nayyar and Rahul Jain).

  • Distributed Computing and Storage: we developed extensions of Fork-Join queueing networks to model large-scale virtualized storage systems (with Indra Widjaja and Iraj Saniee).

We also harbor a latent interest in machine learning and statistical modeling. In particular, we're intrigued by questions relating to model selection - minimum description length, Kolmogorov complexity, high dimensional statistics. If you have a problem to discuss, please contact Prof. Honnappa at honnappa@purdue.edu.