### Plenary Speakers

**Halil Mete Soner**, ETH Zurich, Switzerland

Halil Mete Soner is a professor of mathematics at the Swiss Federal Institute of Technology in Zurich (Eidgenossische Technische Hochschule Zurich). He holds a Senior Chair at the Swiss Finance Institute. His research is concentrated on nonlinear analysis in partial differential equations, stochastic processes and mathematical finance. He co-authored a book, with Wendell Fleming, on viscosity solutions and stochastic control; Controlled Markov Processes and Viscosity Solutions, Springer-Verlag, 1993 (second edition in 2005). |

**Stochastic Target Problems**

In a stochastic target problem, the controller tries to steer a stochastic state process into a prescribed target set with certainty. The state is assumed to follow stochastic dynamics while the target is deterministic and this miss-match renders the problem difficult and without any correlations between the noise process it is not possible to achieve this goal. However, when there are such degeneracies and/or correlations of the noise process, one exploits them to determine the initial positions from which this goal is feasible. These problems appear naturally in several applications in quantitative finance providing robust hedging strategies. As a convenient solution technique, we use the geometric dynamic programming principle that we will describe in this talk. Then, this characterization of the reachability sets will be discussed in several examples.

**John N. Tsitsiklis**, Massachusetts Institute of Technology, US

John N. Tsitsiklis is a Clarence J Lebel Professor of Electrical Engineering, with the Department of Electrical Engineering and Computer Science (EECS) at MIT, affiliated with the Laboratory for Information and Decision Systems (LIDS) and the Operations Research Center (ORC). He is currently serving as the Chair of the Council of the Harokopio University in Greece. His research interests are in the fields of systems, optimization, control, and operations research. He is a coauthor of Parallel and Distributed Computation: Numerical Methods (1989, with D. Bertsekas), Neuro-Dynamic Programming (1996, with D. Bertsekas), Introduction to Linear Optimization (1997, with D. Bertsimas), and Introduction to Probability (1st ed. 2002, 2nd. ed. 2008, with D. Bertsekas). |

**An analysis of sparse, limited flexibility, service architectures**

It is well known that resource pooling (or, equivalently, the use of flexible resources that can serve multiple types of requests) significantly improves the performance of service systems. On the other hand, complete resource pooling often results in higher infrastructure (communication and coordination) costs. This leads us to explore the benefits that can be derived by a limited amount of resource pooling, and the question of whether a limited amount of pooled resources can deliver most of the benefits of complete resource pooling.

We consider a service system with n independent job streams and n servers, where each server can only serve a relatively small number, d, of job streams. We wish to design a service architecture (an assignment of d streams to each server) so that the system has as large a capacity region as possible, and a scheduling policy under which queueing delays become vanishingly small as the system size, n, increases. After reviewing the pros and cons of a simple, modular architecture, we show that our objective can be accomplished by combining an expander graph architecture and a batching policy. This improves upon earlier results that involved a random graph and whose guarantees held only under high probability probabilistic.

(Joint work with Kuang Xu.)

**Kavita Ramanan, Brown University, US**

Kavita Ramanan is a professor at the Division of Applied Mathematics at Brown University. She is a recipient of the Erlang Prize of the INFORMS Applied Probability Society and a fellow of the IMS (Institute for Mathematics and Statistics). Her research lies in the area of probability theory, stochastic processes and their applications, including stochastic analysis, large deviations, Gibbs measures, measure-valued processes and applications to stochastic networks. |

**Infinite-Dimensional Scaling Limits of Stochastic Networks**

Many stochastic networks are too complex to be amenable to an exact analysis. An established framework is instead to obtain tractable approximations that provide qualitative insight into the dynamics and whose accuracy can be rigorously justified in a suitable (asymptotic) regime of network parameters via limit theorems for suitably scaled state processes. It turns out that in many cases, to establish scaling limits it is fruitful to use an infinite-dimensional Markovian representation of the state dynamics. We illustrate this in the context of two different classes of models: randomized load balancing models in the presence of general service times, and single-server networks with scheduling policies (such as Earliest-Deadline-First or Shortest-Remaining-Processing-Time) that employ a continuous parameter to prioritize the service of different jobs. Although the nature of the infinite-dimensional representations is rather different for the two classes of models, we show that they both lead to tractable scaling limits that can be used to identify interesting (and sometimes counter-intuitive) qualitative phenomena. This is based on various joint works with Mohammadreza Aghajani, Rami Atar, Anup Biswas and Haya Kaspi.