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.

Obtaining Dynamic Scheduling Policies with Simulation and Machine Learning

Abstract: Dynamic scheduling of tasks in large-scale HPC platforms is normally accomplished using ad-hoc heuristics, based on task characteristics, combined with some backfilling strategy. Defining heuristics that work efficiently in different scenarios is a difficult task, specially when considering the large variety of task types and platform architectures. In this work, we present a methodology based on simulation and machine learning to obtain dynamic scheduling policies. Using simulations and a workload generation model, we can determine the characteristics of tasks that lead to a reduction in the mean slowdown of tasks in an execution queue. Modeling these characteristics using a nonlinear function and applying this function to select the next task to execute in a queue improved the mean task slowdown in synthetic workloads. When applied to real workload traces from highly different machines, these functions still resulted in performance improvements, attesting the generalization capability of the obtained heuristics.

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.