In this paper, we use dynamic-bubblesort technology to analyze general first-in-first-out K-queue homogenous fork/join queuing (HFJ) systems for any K >; 2. Jobs arrive with a 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 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. We mathematically prove an upper bound solution for the mean response time that we denote by TK. The upper bound solution of general K-queue HFJ systems for any K ≥ 2 is very simple and practical-one only needs to simulate a small number of queues (e.g., 16 queues). The tightness is evaluated by comparing with the simulation of thousands of queues for three different HFJ cases. The maximum offset for our upper bounds over a//the simulations is less than 5 percent. The corresponding source codes (reusable) are offered on our website for others to use.

A new analysis technique, dynamic-bubblesort analysis, is introduced for general K-queue first-in-first-out HFJ (homogenous fork/join queuing) systems of K/spl ges/2 . The dynamic-bubblesort model dynamically sorts the branches of the queues based on the number of the tasks waiting for synchronization in each branch. Jobs arrive with mean rate /spl 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 obtain a general and simple hybrid solution which combines analysis and simulation for the mean response time that we denote by T/sub K/. We obtain a very simple (as a function of T/sub 1/ and T/sub 2/ only) and general upper bound expression for T/sub K/ and we get an exact relationship between the cases for K=2 and 3. We evaluate our results by simulating 2, 3, ..., 99, and 100 queues for p=0.1, 0.2, ....0.8, and 0.9, each for four different HFJ cases, where /spl rho/=/spl lambda///spl mu/ and /spl mu/ is the average task service rate for a server. The maximum absolute offset for our hybrid solutions from all the simulations is less than 0.33 percent (1/300), which is a reasonable error ratio for simulation. The maximum offset for our upper bounds over all the simulations is 21 percent.