A Generalized Performance Evaluation Framework for Parallel Systems with Output Synchronization

by   Wasiur R. KhudaBukhsh, et al.

Frameworks, such as MapReduce and Hadoop are abundant nowadays. They seek to reap benefits of parallelization, albeit subject to a synchronization constraint at the output. Fork-Join (FJ) queuing models are used to analyze such systems. Arriving jobs are split into tasks each of which is mapped to exactly one server. A job leaves the system when all of its tasks are executed. As a metric of performance, we consider waiting times for both work-conserving and non-work conserving server systems under a mathematical set-up general enough to take into account possible phase-type behavior of the servers, and as suggested by recent evidences, bursty arrivals. To this end, we present a Markov-additive process framework for an FJ system and provide computable bounds on tail probabilities of steady-state waiting times, for both types of servers separately. We apply our results to three scenarios, namely, non-renewal (Markov-modulated) arrivals, servers showing phase-type behavior, and Markov-modulated arrivals and services. We compare our bounds against estimates obtained through simulations and also provide a theoretical conceptualization of provisions in FJ systems. Finally, we calibrate our model with real data traces, and illustrate how our bounds can be used to devise provisions.


page 1

page 2

page 3

page 4


Optimizing Stochastic Scheduling in Fork-Join Queueing Models: Bounds and Applications

Fork-Join (FJ) queueing models capture the dynamics of system paralleliz...

Non-Asymptotic Delay Bounds for Multi-Server Systems with Synchronization Constraints

Multi-server systems have received increasing attention with important i...

A Foreground-Background queueing model with speed or capacity modulation

The models studied in the steady state involve two queues which are serv...

System Stability Under Adversarial Injection of Dependent Tasks

In this work, we consider a computational model of a distributed system ...

Product Forms for FCFS Queueing Models with Arbitrary Server-Job Compatibilities: An Overview

In recent years a number of models involving different compatibilities b...

Performance of Balanced Fairness in Resource Pools: A Recursive Approach

Understanding the performance of a pool of servers is crucial for proper...

The Tiny-Tasks Granularity Trade-Off: Balancing overhead vs. performance in parallel systems

Models of parallel processing systems typically assume that one has l wo...

Please sign up or login with your details

Forgot password? Click here to reset