Seminar in applied mathematics and statistics

SPEAKER: Peter Glynn (Stanford)

TITLE: Limit Theorems for Queues in the Presence of Non-renewal Traffic

ABSTRACT:
Much of the mathematical theory for queues has been developed in a setting in which the arriving traffic is assumed to follow a renewal process or some Markov-modulated variant. In this talk, we discuss how queues behave when the traffic is either “scheduled” or “randomly scattered”. A scheduled arrival process is one in which the customers are scheduled to arrive at regularly spaced intervals, but customer-specific behavior induces random perturbations that determine their actual arrival times. Many service facilities use scheduling to “even out” their workload over time. The “random scattering” model is one that pertains to situations where customers choose their own customer-specific time at which to access a resource, as may occur when visiting a website or downloading a daily update to a server farm. In this talk, we describe various limit theorems associated with such arrival models, including heavy traffic limit theory and large deviations results. This work is joint with Victor Araman, Hong Chen, Harsha Honnappa, and Li Xia.

Tea and chocolate will be served in room 04.3.15 after the seminar.

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CURRENT SCHEDULE FOR SPRING 2016:
January 20, 15.15, Aud. 6: Alessia Pini (MOX, Politecnico di Milano)
February 24, 15.15, Aud. 10: Matthias Fahrenwaldt (Hannover)
March 9, 15.15, Aud. 10: Mogens Fosgerau (DTU)
March 11, 14.15, Aud. 8: Hansjoerg Albrecher (Lausanne)
March 16, 15.15, Aud. 10: Peter McCullagh (Oxford/Chicago)
March 17, 15.15, Aud. 10: Peter Glynn (Stanford)