Approximate Analysis of Fork/Join Synchronization in Parallel Queues
IEEE Transactions on Computers
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
Queueing Networks and Markov Chains
Queueing Networks and Markov Chains
Queueing models of RAID systems with maxima of waiting times
Performance Evaluation
Implementing Generating Set Search Methods for Linearly Constrained Minimization
SIAM Journal on Scientific Computing
A simulated annealing driven multi-start algorithm for bound constrained global optimization
Journal of Computational and Applied Mathematics
Delay scheduling: a simple technique for achieving locality and fairness in cluster scheduling
Proceedings of the 5th European conference on Computer systems
Analytical and Simulation Modelling of Zoned RAID Systems
The Computer Journal
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We consider split-merge systems with heterogeneous subtask service times and limited output buffer space in which to hold completed but as yet unmerged subtasks. An important practical problem in such systems is to limit utilisation of the output buffer. This can be achieved by judiciously delaying the processing of subtasks in order to cluster subtask completion times. In this paper we present a methodology to find those deterministic subtask processing delays which minimise any given percentile of the difference in times of appearance of the first and the last subtasks in the output buffer. Technically this is achieved in three main steps: firstly, we define an expression for the distribution of the range of samples drawn from n independent heterogeneous service time distributions. This is a generalisation of the well-known order statistic result for the distribution of the range of n samples taken from the same distribution. Secondly, we extend our model to incorporate deterministic delays applied to the processing of subtasks. Finally, we present an optimisation scheme to find that vector of delays which minimises a given percentile of the range of arrival times of subtasks in the output buffer. A case study illustrates the applicability of our proposed approach.