A Fast Simulation for Thousands of M/2M/2 Parallel Homogeneous Fork/Join Pipelines

Abstract

We study a parallel K-pipeline HFJ (Homogeneous Fork/Join queueing) system in which each pipeline has two identical exponential first-in-first-out services where each service has an infinite capacity queue. Jobs arrive with Poisson arrival distribution. Upon arrival, a job forks into K tasks. Task k, k = 1, 2, ..., K, is assigned to the kth pipeline. A job leaves the HFJ system as soon as all its tasks complete their service. We call the system M/2M/2 HFJ pipelines. In this paper, we present a speed and memory solution to simulate thousands of pipelines in minutes for the mean response time, which we denote by T_K. On a regular DELL INSPIRON 1464-138 laptop with 2G memory, the simulation for 10,000 M/2M/2 HFJ pipelines lasts only 36 minutes for 5 million warm-up jobs and 20 million analysis jobs. As an application, we compare simulation results for K = 2,000 with two mean response time solutions in [1] and [2]. Reusable source code is also offered for others to use.