Is our queue processing speeding up? We have been collecting statistics on a queueing and processing system that powers part of our business. We have multiple servers processing items in a queue.
We recently added new servers, and we want to know whether we're processing faster. By "processing faster", I mean something like this:

Last week, all of our servers processed a combined average of X files/min during our peak load. This week, all of our servers processed a combined average of Y files/min during peak load. Are X and Y different enough to be statistically significant?

The data I have access to looks something like this graph, which shows the number of files processed per second for an hour-long time period. I have access to about 3 months of this type of data.

I have a minor in statistics, but I'm 10 years out of school. So please be gentle :-)
Thanks so much!
Alan
 A: I would consider this a case of interrupted time series analysis. A very simple test to start would be a t-test of mean differences in the number of files processed per minute before the servers were installed versus after they were installed.
If the number of files handled has some seasonality (e.g. if more files are processed during night time than during the daytime, or if more files are processed during summer months than winter months), or if you expect the process to have be correlated in time (e.g. if processing fewer files in the prior period is likely to predict processing fewer files in the current period) you will want to model the seasonal process using ARIMA modelling and then identify if the difference is independent of those seasonal fluctuations and/or ARMA terms. See the arima tag for other questions on how to accomplish this.
If there is no seasonality though (there doesn't appear to be any in the plot you provide) the t-test of mean differences may be sufficient to answer your question.
