Allocating Independent Subtasks on Parallel Processors
IEEE Transactions on Software Engineering
Approximate Analysis of Fork/Join Synchronization in Parallel Queues
IEEE Transactions on Computers
Performance Analysis of Parallel Processing Systems
IEEE Transactions on Software Engineering
Analysis of the Fork-Join Queue
IEEE Transactions on Computers
Acyclic fork-join queuing networks
Journal of the ACM (JACM)
Bounding Availability of Repairable Systems
IEEE Transactions on Computers
A Decomposition Procedure for the Analysis of a Closed Fork/Join Queueing System
IEEE Transactions on Computers
Approximate solutions for M/G/1 fork/join synchronization
WSC '94 Proceedings of the 26th conference on Winter simulation
Interpolation approximations for symmetric Fork-Join queues
Performance '93 Proceedings of the 16th IFIP Working Group 7.3 international symposium on Computer performance modeling measurement and evaluation
IEEE Transactions on Computers
Performance Analysis and Scheduling of Stochastic Fork-Join Jobs in a Multicomputer System
IEEE Transactions on Parallel and Distributed Systems
Computing Performance Bounds of Fork-Join Parallel Programs Under a Multiprocessing Environment
IEEE Transactions on Parallel and Distributed Systems
Analysis and simulation of parallel fork-join systems
Analysis and simulation of parallel fork-join systems
Theory, Volume 1, Queueing Systems
Theory, Volume 1, Queueing Systems
Modeling parallel and distributed systems with finite workloads
Performance Evaluation - Performance modelling and evaluation of high-performance parallel and distributed systems
On the probability distribution of join queue length in a fork-join model
Probability in the Engineering and Informational Sciences
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A new analysis technique, dynamic-bubblesort analysis, is introduced for general K-queue first-in-first-out HFJ (homogenous fork/join queuing) systems of $K \geq 2$. 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 $\lambda$ and a general arrival distribution. Upon arrival, a job forks into K tasks. Task k, $k = 1, 2,\ldots, K$, 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 $T_K$. We obtain a very simple (as a function of $T_1$ and $T_2$ only) and general upper bound expression for $T_K$ and we get an exact relationship between the cases for $K =2$ and 3. We evaluate our results by simulating $2, 3, \ldots, 99$, and 100 queues for $\rho = 0.1, 0.2,\ldots, 0.8$, and 0.9, each for four different HFJ cases, where $\rho =\lambda/\mu$ and $\mu$ 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. Also, we compare our results with three recent papers [19], [20], [22].