**SIMPLIFICATION OF HYPERGAMMA DISTRIBUTION FOR CLUSTER PARALLEL WORKLOAD APPROXIMATION**

**UDC 004.942 **

S. V. Gaevoy, W. M. A. Ahmed, S. A. Fomenkov

In this paper computing clusters (CC) are considered. They are used to execute incoming jobs. There is such a CC in our university and we need to predict its service characteristics at executing several workloads. An important method to analyze parallel workloads is modeling execution of those systems by using parallel workload models (PWM). We use PWMs to model the CC in order to get these service characteristics. We have already proposed many PWMs, but all these PWMs use a continuous variable approximation. This approximation can be done either by method of moments (MM), or maximum likelihood method (MLM). The latter gives the more accurate results but consumes much time. The best distributions for the approximation are Hyperexpoential and Hypergamma distributions. It was empirically proved in our and third-party papers. The simplification we have already proposed reduces the time consumption of the Hyperexponential distribution by using MM instead of MLM. In this paper a simplified method of Hypergamma distribution approximation is proposed. It reduces the number of the approximated distribution’s parameters and then uses MM or MLM. Hypergamma distribution is chosen, because it has given the best result among all used distributions including Hyperexponential. Nevertheless the proposed method uses our early proposed simplification for Hyperexponential distribution. To validate the quality of the results described in this paper we use the simulation of this approximation and compare the results with the original workload (from the log) in this paper. The characteristics of the proposed methods are demonstrated. The necessity to select an appropriate approximation method is justified.

**Keywords: ** :Method of Moments, Maximum Likelihood Method, parallel workloads, rigid jobs, simulation, stochastic approximation, Hypergamma distribution.

**Full text:**

GaevoyAhmedFomenkov_1_1_18.pdf