A Mathematical Model for Cluster Applications

Mohamed I. Riffi


In this paper, we use probabilistic modeling and techniques to derive formulas in order to determine the number of computer nodes needed to execute applications on a cluster of computers so that application response time can be satisfied. Our probabilistic model is basically an M/G/1/K queueing system.  In this model, we account for the workload conditions (in terms of the number of applications or jobs being received per unit time) as well as the processing power of each node.  Finally, We use simulations to present a numerical example showing how our probabilistic model can be used.

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Bader, D., and Pennington, R. Cluster Computing: Applications (1996, June). Retrieved July 13, 2007, from Georgia Tech College of Computing.

William, W., Hargrove, and Forrest, M. H. Cluster Computing: Linux Taken to the Extreme (1999). Retrieved October 18, 2011, from Linux magazine.

Salah, K. Analysis of a Two-Stage Network Server. International Journal of Applied Mathematics and Computation, Elsevier Science, 217(23), (2011) 9634-9645.

Karam, M., and Tobagi, F. Analysis of Delay and Delay Jitter of Voice Traffic in the Internet. Computer Networks Magazine, 40(6), (2002) 711-726.

Leland, W., Taqqu, M., Willinger, W., and Wilson, D. On the Self-Similar Nature of Ethernet Traffic. IEEE/ACM Transaction on Networking, 2(1), (1994) 1-15.

Jain, R. The Art of Computer Systems Performance Analysis: Techniques for Experimental Design, Measurement, Simulation, and Modeling. Jonh Wiley & Sons, Inc., New York, USA (1991).

Takagi, H. Queueing Analysis: Finite Systems. Vol. 1, North-Holland, Amsterdam, The Netherlands (1993).


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