Workstation Cluster and PVM

Another set of experiments were conducted in two kinds of workstation clusters. The first one was a cluster of six heterogeneous PC's with the Linux operating system. The background load of computers was 'light' but hardly controllable. The second computer system was dedicated (i.e. 'single user') pool of six IBM SP-2 processors. A Parallel Virtual Machine (PVM) was used as a software environment for experiments. We present the final results of the experiments only. A detailed description is given in [DD97]. The star architecture was chosen, and communication models depicted in Fig.4(a) (equations (6)), which we will call Model 1, and Fig.4(b) (equations (7)), which will be called Model 2, were assumed. The application analyzed was distributed file compression using the LZW method [W84,ZL78]. It is typical of the application that the compression ratio depends on the size and contents of the compressed file. The bigger the file the better was the compression obtained. Hence, in further experiments PEs received data in chunks of at least 10kB, which was enough to make the compression ratio relatively stable. Therefore, it was justified to assume in equations (6) and (7) that function $\beta(x)$ of the amount of returned results for $x$ units of data was $\beta(x)=cx$. The coefficient $c=0.55$ was measured experimentally (with standard deviation 9%). Similarly to the previous experiments, computer processing rates, communication transfer rates and startup times were measured experimentally. We believe that communication parameters are relatively stable because the standard deviation of transmission times was below $3\%$ in SP-2 system, and below $5\%$ in the Linux cluster. Unfortunately, this was not the case for processing rate parameters. In the Linux cluster the maximum deviation, depending on the computer, ranged from $23\%$ to $28\%$. In the SP-2 computer standard deviation was below $23\%$. In both computer systems processing rate measurements became more stable with increasing size of the compressed test file. The results of the experiments in both computer clusters and for the two considered models of returning results are collected in Fig.9.

Figure 9: Relative difference between the expected and measured execution time vs size $V$ of the compressed file in Model 1: a)Linux, b)IBM SP-2, and Model 2: c)Linux, d)IBM SP-2.

As it can be seen, in the Linux cluster the difference is below 25% in Model 1, and below 35% in Model 2. In the dedicated pool of SP-2 processors the difference is more stable and remains between 5% and 15%. The sources of the difference between the theoretical model and the reality can be imprecision in the parameters $A_i, C_i, S_i$ and function $\beta(x)$.

We infer that the divisible task concept can be a useful model for distributed applications. Though the model is crude and neglects many details of actual computer systems, a practical verification proved viability of its principles.