Efficient Response Time Approximations for Multiclass Fork and Join Queues in Open and Closed Queuing Networks

Parallel and concurrent structures are widely used both as standalone components and as building blocks of larger systems. Efficient models of parallelism and concurrency are therefore necessary to understand the impact of parallelism in system performance. These models become more critical with the proliferation of adaptive systems that require solving a large number of performance models in a short amount of time to facilitate configuration decisions dynamically. This paper presents efficient response time approximations for parallel constructs modeled as fork and join queues. These approximations can be used by practitioners and performance engineers to quickly compare the performance of contending configurations. The contributions over previous work are twofold. First, this paper considers heterogeneous multiclass fork and join open and closed queuing networks. Second, the paper also presents models for fork and join where each class of jobs might fork to different queues in a probabilistic manner.