The seminar is sponsored by NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai.
Abstract:
Load balancing with various type of load information has become a key component of modern communication and information systems. Recently, a renewed interest has been given to mean-field properties of systems where the load and the number of servers scales jointly, allowing to give insights on the behavior of very large systems.
We address here the problem of giving robust performance bounds based on studying the asymptotic behavior of the so-called insensitive load balancing schemes. These schemes have the desirable property that the stationary distribution of the resulting stochastic network depends on the distribution of job sizes only through its mean and it was shown that they might give good estimates of performance indicators whereas for networks of moderate size, optimal policies are already theoretically and computationally out of reach.
We first theoretically characterize these schemes. Then, we study the case of a single class of traffic for arbitrary large systems and we characterize under various regime of load, using functional law of large numbers and large deviations, the response of symmetric systems under those schemes. In particular, we show that there is a phase transition for the blocking probability.
Before a critical load depending on the buffer depths and the number of servers, the blocking is exponentially small and becomes of polynomial order at the critical load.
This generalizes the well-known Jagerman-Halfin-Whitt regime for a one-dimensional queue. It also gives a generalized staffing rule for a given target blocking probability.
Biography:
Matthieu Jonckheere received a Ph.D. in Applied Mathematics from the Ecole Polytechnique (Paris), did a post-doc in CWI (Amsterdam), and was an assistant professor at the University of Eindhoven, after which he became a Conicet researcher and then professor at the University of Buenos Aires. His research focuses on stochastic networks, particles systems, quasi-stationary distributions, and information processing in high dimension.