Calendar

In multi-server distributed queueing systems, the access of stochastically arriving jobs to resources is often regulated by a dispatcher. A fundamental problem consists in designing a load balancing algorithm that minimizes the delays experienced by jobs. During the last two decades, the power-of-d-choice algorithm, based on the idea of dispatching each job to the least loaded server out of $d$ servers randomly sampled at the arrival of the job itself, has emerged as a breakthrough in the foundations of this area due to its versatility and appealing asymptotic properties. We consider the power-of-d-choice algorithm with the addition of a local memory that keeps track of the latest observations collected over time on the sampled servers. Then, each job is sent to a server with the lowest observation. We show that this algorithm is asymptotically optimal in the sense that the load balancer can always assign each job to an idle server in the large-server limit. This holds true if and only if the system load $\lambda$ is less than $1-\frac{1}{d}$. If this condition is not satisfied, we show that queue lengths are bounded by $j^\star+1$, where $j^\star\in\mathbb{N}$ is given by the solution of a polynomial equation. This is in contrast with the classic version of the power-of-d-choice algorithm, where queue lengths are unbounded. Our upper bound on the size of the most loaded server, $j^*+1$, is tight and increases slowly when $\lambda$ approaches its critical value from below. For instance, when $\lambda= 0.995$ and $d=2$ (respectively, $d=3$), we find that no server will contain more than just $5$ ($3$) jobs in equilibrium. Our results quantify and highlight the importance of using memory as a means to enhance performance in randomized load balancing.

Abstract:
In this talk, we will introduce a new class of stochastic multilayer networks. A stochastic multilayer network is the aggregation of M networks (one per layer) where each is a subgraph of a foundational network G. Each layer network is the result of probabilistically removing links and nodes from G. The resulting network includes any link that appears in at least K layers. This model, which is an instance of a non-standard site-bond percolation model, finds applications in wireless communication networks with multichannel radios, multiple social networks with overlapping memberships, transportation networks, and, more generally, in any scenario where a common set of nodes can be linked via co-existing means of connectivity. Percolation, exact and asymptotic results will be presented.

The polyhedral model has proven to be very useful to optimize and parallelize a particular class of compute intensive application kernels. A polyhedral optimizer needs to have affine functions defining loop bounds, memory accesses and branching conditions. Unfortunately, this information is not always available at compile time. To broaden the scope of polyhedral optimization opportunities, runtime information can be considered. This talk will highlight the challenges of integrating polyhedral optimization in runtime systems:

- When and how to detect opportunities for polyhedral optimization?
- How to model the observed runtime behavior in a polyhedral fashion?
- How to deal at runtime with the complexity of polyhedral algorithm?

These challenges will be illustrated in the context of both the APOLLO framework targeting C and C++ applications and of the JavaScript engine from Apple.

Resource allocation games are commonly used to model problems in many domains ranging from security to advertising. One of the most important resource allocation games is the Colonel Blotto game: Two players distribute a fixed budget of resources over multiple battlefields to maximize the aggregate value of battlefields they win, each battlefield being won by the player who allocates more resources to it. Despite its long-standing history and importance, the continuous version of the game---where players can choose any fractional allocation---still lacks a complete Nash equilibrium solution in its general form with asymmetric players' budgets and heterogeneous battlefield values.

In this work, we propose an approximate equilibrium for this general case. We construct a simple strategy (the independently uniform strategy) and prove that it is an epsilon-equilibrium. We give a theoretical bound on the approximation error in terms of the number of battlefields and players’ budgets which identifies precisely the parameters regime for which our strategy is a good approximation. We also investigate an extension to the discrete version (where players can only have integer allocations), for which we proposed an algorithm to compute very efficiently an approximate equilibrium. We perform numerical experiments that guarantee that we can "safely" use this strategy in practice. Our work extends the scope of application of Colonel Blotto games in several practical cases, especially with large games' parameters (e.g. in advertisements, voting, security, etc.,)