Wasiur R. KhudaBukhsh

Optimizing stochastic scheduling in fork-join queueing models: Bounds and applications

Fork-Join (FJ) queueing models capture the dynamics of system parallelization under synchronization constraints, for example, for applications such as MapReduce, multipath transmission and RAID systems. Arriving jobs are first split into tasks and mapped to servers for execution, such that a job can only leave the system when all of its tasks are executed. In this paper, we provide computable stochastic bounds for the waiting and response time distributions for heterogeneous FJ systems under general parallelization benefit. Our main contribution is a generalized mathematical framework for probabilistic server scheduling strategies that are essentially characterized by a probability distribution over the number of utilized servers, and the optimization thereof. We highlight the trade-off between the scaling benefit due to parallelization and the FJ inherent synchronization penalty. Further, we provide optimal scheduling strategies for arbitrary scaling regimes that map to different levels of parallelization benefit. One notable insight obtained from our results is that different applications with varying parallelization benefits result in different optimal strategies. Finally, we complement our analytical results by applying them to various applications showing the optimality of the proposed scheduling strategies.

Analysing and leveraging client heterogeneity in swarming-based live streaming

Due to missing IP multicast support on an Internet scale, over-the-top media streams are delivered with the help of overlays as used by content delivery networks and their peer-to-peer (P2P) extensions. In this context, mesh/pull-based swarming plays an important role either as a pure streaming approach or in combination with tree/push mechanisms. The crucial impact of todays variety of client systems with their heterogeneous resources is not yet well understood. In this paper, we contribute to closing this gap by mathematically analysing the most basic scheduling mechanisms latest deadline first (LDF) and earliest deadline first (EDF) in a continuous time Markov chain framework and combining them into a simple, yet powerful, mixed strategy to leverage inherent differences in client resources. The contribution of this paper is, hence, twofold: (1) we develop a mathematical framework for swarming on random graphs with a focus on LDF and EDF strategies in heterogeneous scenarios; (2) we propose a mixed strategy, named SchedMix, that leverages client heterogeneity. We show that SchedMix outperforms LDF and EDF using different abstractions: a mean-field theoretic analysis of buffer probabilities, simulations of the stochastic model on random graphs, and a full-stack implementation of a P2P streaming system.