Modeling the Performance of Computer Intensive Applications of a Parallel Computer O. E. Oguike 1 and M.N Agu 2 S.C. Echezona 3 and D.U. Ebem 4 Department of Computer Science, University of Nigeria, Nsukka, Enugu State, Nigeria. e-mail: 1 osondu.oguike@unn.edu.ng 2 monica.agu@unn.edu.ng 3 stevenson.echezona@unn.edu.ng , 4 deborah.ebem@unn.edu.ng Abstract— From the queuing system approach, a compute intensive application can be defined as any application where the arrival rate of processes into the processors queue is greater than the overall departure rate of the processes from the processors. Such a compute intensive application is ideal for a parallel computer because there are always processes for the processors to execute. This paper, therefore, aims at using a novel and efficient queuing approach to model some of the performance metrics of the parallel processors, for compute intensive applications. Keywords- Queuing System; Performance Metrics; Compute Intensive Applications; Modeling; Average Turnaround Time, Average Waiting Time, Percentage of Utilization of the CPUs. I. INTRODUCTION Compute intensive application of a parallel computer can be defined based on queuing system, as any application of the parallel computer where the arrival rate of processes is greater than the service/execution rate of all the processors. A shared memory parallel computer system can consist of finite, single ready queue. Since the memory is shared, we assume that the shared memory is large enough to accommodate jobs that arrive. The assumptions to be made about the system is that there are C parallel processors and a finite single ready queue [7,12,4,13] The arrival of processes into the finite, single ready queue is assumed to have poisson distribution and the service time has exponential distribution.[3, 14] The diagram below illustrates a single queue, parallel server model of a parallel computer. C Parallel Processors CPUs Queue Figure 1. Single Queue, Parallel Server Model of a Parallel Computer II. STATEMENT OF THE PROBLEM The service/departure rate for a single queue, parallel server queuing model in the literature [6] cannot be applied to a compute intensive, parallel computer application. The service/departure rate has been modeled in literature as ｰ ｯ ｰ ｮ ｭ      otherwise X x C C C x x x , 0 , 0 , P P P where X is the maximum number of processes that can be in the system. The above service/execution rate does not truly represent the service rate or execution rate of a compute intensive, parallel computer application, where all the processors are busy at all time, executing a part of a program at the same time. There is therefore the need to redefine the service/execution rate of a compute intensive, parallel computer application. Furthermore, modeling some performance metrics, using the traditional probability density function that considers the whole queuing system [6] may not be as efficient as using the Second International Conference on Computational Intelligence, Modelling and Simulation 978-0-7695-4262-1/10 $26.00 © 2010 IEEE DOI 10.1109/CIMSiM.2010.38 457 Second International Conference on Computational Intelligence, Modelling and Simulation 978-0-7695-4262-1/10 $26.00 © 2010 IEEE DOI 10.1109/CIMSiM.2010.38 507 Second International Conference on Computational Intelligence, Modelling and Simulation 978-0-7695-4262-1/10 $26.00 © 2010 IEEE DOI 10.1109/CIMSiM.2010.38 507