On the comparison of mean object size in M/G/1/PS model and M/BP/1 model for web service

This paper aims to compare the mean object size of M/G/1/PS model with that of M/BP/1 model used in the web service. The mean object size is one of important measure to control and manage web service economically. M/G/1/PS model utilizes the processor sharing in which CPU rotates in round-robin order giving time quantum to multiple tasks. M/BP/1 model uses the Bounded Pareto distribution to describe the web service according to file size. We may infer that the mean waiting latencies of M/G/1/PS and M/BP/1 model are equal to the mean waiting latency of the deterministic model using the round robin scheduling with the time quantum. Based on the inference, we can find the mean object size of M/G/1/PS model and M/BP/1 model, respectively. Numerical experiments show that when the system load is smaller than the medium, the mean object sizes of the M/G/1/PS model and the M/BP/1 model become the same. In particular, when the shaping parameter is 1.5 and the lower and upper bound of the file size is small in the M/BP/1 model, the mean object sizes of M/G/1/PS model and M/BP/1 model are the same. These results confirm that it is beneficial to use a small file size in a web service.