How great would this be: I tell you how busy I expect my system to get, and then you tell me how long my users will have to wait. Pretty nice, right? Because then you could help me decide how powerful a system I’d have to buy, and how much total work I could do. Well, there’s a whole branch of mathematics called queueing theory that is devoted to helping you do just that.
Here is a plot of a queueing theory model called M/M/2,1 which is a good model for predicting the behavior of Kevin’s mirrored SSD array. It would also be a good model for, say, a two-lane highway, a public restroom with two stalls, or a bank with two tellers. The number “2” in “M/M/2” is the service channel count. A service channel is a resource that services requests; for example, an SSD, a lane, a stall, or a teller.
This plot shows expected response time (R) as a function of traffic intensity (ρ), which is a measure from 0 to 1 of how busy the system is.2 I’ve drawn the data from Kevin’s SSD story in the plot: R = Q + S = 4.5 S, where Q = 3.5 S is the expected queueing delay, and S is the expected service time. You could substitute the actual service time (0.000 464 seconds) for the symbol S, but it’s easier to understand what’s going on if you use S as the unit. That’s why I’ve laid out the vertical axis in units of S.
Generally, the model reveals:
Increasing the load on a system ...
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