Analysis and Simulation for a Mean Response Time Hybrid Solution to Homogeneous Fork/Join Queues

Abstract

In this paper, we simulate and analyze general K-queue HFJ (Homogeneous Fork/Join) systems with 100-thousand parallel queues for the mean response time, which we denote by T[K]. Jobs arrive with mean rate lambda and a general arrival distribution. Upon arrival, a job forks into K tasks. Task k, k = 1, 2, K, is assigned to the kth queuing system, which is a first-in-first-out server with a general service distribution and an infinite capacity queue. A job leaves the HFJ system as soon as all its tasks complete their service. In other words, tasks corresponding to the same job are joined before departing the HFJ system. We use the huge-scale simulation to analyze the tightness and the trend of a mean response time hybrid solution [1] as K grows. The hybrid solution is consistent for huge-scale systems with max absolute offset.