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

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 λ and a general arrival distribution. Upon arrival, a job forks into K tasks. Task k, k = 1, 2, ..., K, is assigned to the k^th 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 as K grows. The hybrid solution is consistent for huge-scale systems with max absolute offset <; 0.5%. In general, the max offsets and the min offsets do not change significantly as the scale (the number of queues) increases.