What are logarithmic normal variables

Why does a log normal distribution fit well with server response times?

I found that web server response times are typically modeled here as from a log normal distribution. What I don't quite understand is why this is the case!

In particular, Wikipedia states that a random variable X is logarithmically normally distributed if it has that product of several independent normal variables.

In that case, what would these single normal variables represent in the execution time of the server code?

I haven't found any sources discussing why the log normal distribution fits well with the web server's response times.

Not sure if this question is best asked at stackoverflow or math.stackexchange, but thought I'd give it a try here.

Thank you for every insight!


You might want to read the paper

Vern Paxson. Empirically derived analytical models of large area TCP connections. IEEE / ACM transactions on the network, 1994.

which is available online here. From the summary:

We analyze 3 million TCP connections that occurred during 15 large-area traffic lanes. The traces were collected in five “stub” networks and two internetwork gateways in order to provide a diverse view of the large-scale traffic. We derive analytical models that describe the random variables associated with Telnet, Nntp, SMTP, and FTP connections.

and from the paper

For most connections, the responder / duration ratio was modeled well by an exponential distribution, but “large” connections - those with responder bytes in the top 10% of all connections - had a different distribution. For these, the ratio was modeled fairly well by a log normal distribution.

However, it is a bit out of date :-)

Tell me. You don't know the distribution, but you don't have to. According to the central limit theorem. Don't worry about the parameters. Then. Last part: .X.1,… Xn∼ii detwasX.¯ → N.exp (X.¯) → lognormalY1 = exp (∑iXin) = [exp (∑iXi)] 1 / n = [∏iexpXi] 1 / n

Y1 is your first response time. I don't know about this stuff, but your justification for it probably has something to do with it. Chances are your response rate comes from an average of a million unknown things that came from an unknown distribution.

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