Resource augmentation in load balancing

We consider load-balancing in the following setting. The on-line algorithm is allowed to use $n$ machines, whereas the optimal off-line algorithm is limited to $m$ machines, for some fixed $m < n$. We show that while the greedy algorithm has a competitive ratio which decays linearly in the inverse of $n/m$, the best on-line algorithm has a ratio which decays exponentially in $n/m$. Specifically, we give an algorithm with competitive ratio of 1+2^{- frac{n{m (1- o (1)), and a lower bound of 1+ e^{ - frac{n{m (1+ o(1)) on the competitive ratio of any randomized algorithm. We also consider the preemptive case. We show an on-line algorithm with a competitive ratio of 1+ e^{ - frac{n{m (1+ o(1)). We show that the algorithm is optimal by proving a matching lower bound. We also consider the non-preemptive model with temporary tasks. We prove that for $n=m+1$, the greedy algorithm is optimal. (It is not optimal for permanent tasks.

RepFlow: Minimizing Flow Completion Times with Replicated Flows in Data Centers

Short TCP flows that are critical for many interactive applications in data centers are plagued by large flows and head-of-line blocking in switches. Hash-based load balancing schemes such as ECMP aggravate the matter and result in long-tailed flow completion times (FCT). Previous work on reducing FCT usually requires custom switch hardware and/or protocol changes. We propose RepFlow, a simple yet practically effective approach that replicates each short flow to reduce the completion times, without any change to switches or host kernels. With ECMP the original and replicated flows traverse distinct paths with different congestion levels, thereby reducing the probability of having long queueing delay. We develop a simple analytical model to demonstrate the potential improvement of RepFlow. Extensive NS-3 simulations and Mininet implementation show that RepFlow provides 50%--70% speedup in both mean and 99-th percentile FCT for all loads, and offers near-optimal FCT when used with DCTCP.Comment: To appear in IEEE INFOCOM 201

Runtime support for load balancing of parallel adaptive and irregular applications

Applications critical to today\u27s engineering research often must make use of the increased memory and processing power of a parallel machine. While advances in architecture design are leading to more and more powerful parallel systems, the software tools needed to realize their full potential are in a much less advanced state. In particular, efficient, robust, and high-performance runtime support software is critical in the area of dynamic load balancing. While the load balancing of loosely synchronous codes, such as field solvers, has been studied extensively for the past 15 years, there exists a class of problems, known as asynchronous and highly adaptive , for which the dynamic load balancing problem remains open. as we discuss, characteristics of this class of problems render compile-time or static analysis of little benefit, and complicate the dynamic load balancing task immensely.;We make two contributions to this area of research. The first is the design and development of a runtime software toolkit, known as the Parallel Runtime Environment for Multi-computer Applications, or PREMA, which provides interprocessor communication, a global namespace, a framework for the implementation of customized scheduling policies, and several such policies which are prevalent in the load balancing literature. The PREMA system is designed to support coarse-grained domain decompositions with the goals of portability, flexibility, and maintainability in mind, so that developers will quickly feel comfortable incorporating it into existing codes and developing new codes which make use of its functionality. We demonstrate that the programming model and implementation are efficient and lead to the development of robust and high-performance applications.;Our second contribution is in the area of performance modeling. In order to make the most effective use of the PREMA runtime software, certain parameters governing its execution must be set off-line. Optimal values for these parameters may be determined through repeated executions of the target application; however, this is not always possible, particularly in large-scale environments and long-running applications. We present an analytic model that allows the user to quickly and inexpensively predict application performance and fine-tune applications built on the PREMA platform