Quantitative system performance: computer system analysis using queueing network models
Quantitative system performance: computer system analysis using queueing network models
Approximate Analysis of Fork/Join Synchronization in Parallel Queues
IEEE Transactions on Computers
Analysis of the Fork-Join Queue
IEEE Transactions on Computers
Acyclic fork-join queuing networks
Journal of the ACM (JACM)
On the execution of parallel programs on multiprocessor systems—a queuing theory approach
Journal of the ACM (JACM)
A Decomposition Procedure for the Analysis of a Closed Fork/Join Queueing System
IEEE Transactions on Computers
An analytic performance model of disk arrays
SIGMETRICS '93 Proceedings of the 1993 ACM SIGMETRICS conference on Measurement and modeling of computer systems
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
Analysis of balanced fork-join queueing networks
Proceedings of the 1996 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Bound Performance Models of Heterogeneous Parallel Processing Systems
IEEE Transactions on Parallel and Distributed Systems
Mean value technique for closed fork-join networks
SIGMETRICS '99 Proceedings of the 1999 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
Mean-Value Analysis of Closed Multichain Queuing Networks
Journal of the ACM (JACM)
Probability and Statistics with Reliability, Queuing and Computer Science Applications
Probability and Statistics with Reliability, Queuing and Computer Science Applications
IEEE Transactions on Computers
Performance Analysis and Scheduling of Stochastic Fork-Join Jobs in a Multicomputer System
IEEE Transactions on Parallel and Distributed Systems
RAID5 Performance with Distributed Sparing
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
A Response Time Distribution Model for Zoned RAID
ASMTA '08 Proceedings of the 15th international conference on Analytical and Stochastic Modeling Techniques and Applications
Modelling Zoned RAID Systems Using Fork-Join Queueing Simulation
EPEW '09 Proceedings of the 6th European Performance Engineering Workshop on Computer Performance Engineering
Using bulk arrivals to model I/O request response time distributions in zoned disks and RAID systems
Proceedings of the Fourth International ICST Conference on Performance Evaluation Methodologies and Tools
A study of the convergence of steady state probabilities in a closed fork-join network
ATVA'10 Proceedings of the 8th international conference on Automated technology for verification and analysis
Closed form approximations for steady state probabilities of a controlled fork-join network
ICFEM'10 Proceedings of the 12th international conference on Formal engineering methods and software engineering
On parametric steady state analysis of a generalized stochastic petri net with a fork-join subnet
PETRI NETS'11 Proceedings of the 32nd international conference on Applications and theory of Petri Nets
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Fork-join structures have gained increased importance in recent years as a means of modeling parallelism in computer and storage systems. The basic fork-join model is one in which a job arriving at a parallel system splits into K independent tasks that are assigned to K unique, homogeneous servers. In this paper, a simple response time approximation is derived for parallel systems with exponential service time distributions. The approximation holds for networks modeling several devices, both parallel and nonparallel. (In the case of closed networks containing a stand-alone parallel system, a mean response time bound is derived.) In addition, the response time approximation is extended to cover the more realistic case wherein a job splits into an arbitrary number of tasks upon arrival at a parallel system. Simulation results for closed networks with stand-alone parallel subsystems and exponential service time distributions indicate that the response time approximation is, on average, within 3 percent of the seeded response times. Similarly, simulation results with nonexponential distributions also indicate that the response time approximation is close to the seeded values. Potential applications of our results include the modeling of data placement in disk arrays and the execution of parallel programs in multiprocessor and distributed systems.