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Performance analysis and scheduling of stochastic fork-join jobs in a multicomputer system

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2 Author(s)
Kumar, A. ; Dept. of Electr. Commun. Eng., Indian Inst. of Sci., Bangalore, India ; Shorey, R.

The authors model a parallel processing system comprising several homogeneous computers interconnected by a communication network. Jobs arriving to this system have a linear fork-join structure. Each fork of the job gives rise to a random number of tasks that can be processed independently on any of the computers. Since exact analysis of fork-join models is known to be intractable, the authors resort to obtaining analytical bounds to the mean job response time of the fork-join job. For jobs with a single fork-join and, probabilistic allocation of tasks of the job to the N processors, they obtain upper and lower bounds to the mean job response time. Upper bounds are obtained using the concept of associated random variables and are found to be a good approximation to the mean job response time. A simple lower bound is obtained by neglecting queueing delays. They also find two lower bounds that include queueing delays. For multiple fork-join jobs, they study an approximation based on associated random variables. Finally, two versions of the join-the-shortest-queue (JSQ) allocation policy (i.e., JSQ by batch and JSQ by task) are studied and compared, via simulations and diffusion limits

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Parallel and Distributed Systems, IEEE Transactions on  (Volume:4 ,  Issue: 10 )