tag:blogger.com,1999:blog-6977755959349847093.post149138463519234486..comments2024-03-01T21:53:15.921-08:00Comments on The Pith of Performance: On the Accuracy of Exponentials and ExpositionsNeil Guntherhttp://www.blogger.com/profile/11441377418482735926noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-6977755959349847093.post-780902881915459792012-03-22T10:28:30.562-07:002012-03-22T10:28:30.562-07:00Matteo, I'm not about to debug your code here ...Matteo, I'm not about to debug your code here but, if you are starting with a table of Exp values and by "rotation" you actually mean pivoting about the <b>diagonal</b> if the xy-axes then, reading off using a uniform dsn is the same as coin flipping and should produce Exp-distd variates.<br /><br />In other words, it sounds like you are implementing the inverse transform, described in my <a href="http://perfdynamics.blogspot.com/2012/03/how-to-generate-exponential-delays.html" rel="nofollow">blog post</a>, as a lookup table.Neil Guntherhttps://www.blogger.com/profile/11441377418482735926noreply@blogger.comtag:blogger.com,1999:blog-6977755959349847093.post-69008725354802678172012-03-22T08:51:23.464-07:002012-03-22T08:51:23.464-07:00errata corrige:
...with a range from 0 to y...
sho...errata corrige:<br />...with a range from 0 to y...<br />should be<br />...with a range from 0 to x...Matteohttps://www.blogger.com/profile/04543214611852575232noreply@blogger.comtag:blogger.com,1999:blog-6977755959349847093.post-55092228347247117662012-03-22T08:33:04.719-07:002012-03-22T08:33:04.719-07:00Hi Dr Gunther,
I've seen your new post, it see...Hi Dr Gunther,<br />I've seen your new post, it seems should be easy to include a development on the tools of they wanted to. Meanwhile I tried to see if my original idea was feasible with a simulation. Central limit theorem should apply when the summed ramdom variables have the same average. In this case I tried to do something like this, http://tinyurl.com/79bd88z, rotated by 90 degrees clockwise. I've loaded the data (x, y) from a exp dsn (generated with excel) into a table and run a script to generate, for each x, a set of random uniform numbers (to fulfill each sub rectangle area as per the picture) with a range from 0 to y. I then summed the occurrences for each x and the graph resembles the original exponential curve. <br />This is the PL/SQL code I used:<br />---------------------<br />declare<br /> type tab is table of number index by binary_integer;<br /> l_t tab;<br /> l_n number;<br /> i number;<br /> j number;<br />begin<br /> for a in (select x, round((exp_dsn - nvl(lag(exp_dsn) over(order by x desc),0))*x*1000) ex from mat_exp order by x desc) loop<br /><br /> for i in 1..a.ex loop<br /> select abs(mod(dbms_random.random, a.x)) into l_n from dual;<br /> if (l_t.exists(l_n)) then<br /> l_t(l_n):= l_t(l_n) +1;<br /> else<br /> l_t(l_n):= 0;<br /> end if;<br /> end loop;<br /> end loop;<br /> <br /> for j in (select x from mat_exp order by x) loop<br /> dbms_output.put_line(to_char(j.x)||'='||l_t(j.x));<br /> <br /> end loop;<br />end; <br />----------------<br /><br />Sorry for not using R.<br />How much wrong is this approach? :-)<br /><br />Thanks<br />Regards<br />MatteoPMatteohttps://www.blogger.com/profile/04543214611852575232noreply@blogger.comtag:blogger.com,1999:blog-6977755959349847093.post-44311716452254440002012-03-21T13:37:04.682-07:002012-03-21T13:37:04.682-07:00For more details about how to generate exponential...For more details about how to generate <b>exponentially distributed delays</b>, see my <a href="http://perfdynamics.blogspot.com/2012/03/how-to-generate-exponential-delays.html" rel="nofollow">latest blog post</a>.Neil Guntherhttps://www.blogger.com/profile/11441377418482735926noreply@blogger.comtag:blogger.com,1999:blog-6977755959349847093.post-72093727748579325102012-03-20T10:42:15.763-07:002012-03-20T10:42:15.763-07:00Hi Matteo, Interesting idea, but I suspect it will...Hi Matteo, Interesting idea, but I suspect it will be thwarted by a well-known theorem in probability theory, which states roughly that adding the resulting collection metrics (random variables with whatever underlying dsn---uniform in your suggestion) will merely tend to emulate a Normal dsn. And that is arguably <b>less</b> effective than a uniform dsn.Neil Guntherhttps://www.blogger.com/profile/11441377418482735926noreply@blogger.comtag:blogger.com,1999:blog-6977755959349847093.post-29262747610291483932012-03-20T04:30:37.131-07:002012-03-20T04:30:37.131-07:00Hi Dr Gunther, I agree with your comment on load t...Hi Dr Gunther, I agree with your comment on load tools that do not implement exponential distribution to generate the workload. Do you think is it possible to emulate an exponential distribution of requests by combining more runs of a tools in parallel using another distribution (e.g. uniform), different average and different quantities? I was thinking something like: <br />to emulate 10 requests per seconds<br /> run 1: 10 events with delay 1 sec<br />run 2: 18 events with delay 2 sec<br />run 3: 25 events with delay 3 sec<br />etc.<br /><br />Thanks<br />Regards<br />MatteoPMatteohttps://www.blogger.com/profile/04543214611852575232noreply@blogger.comtag:blogger.com,1999:blog-6977755959349847093.post-33898590716677184542012-03-18T22:09:47.292-07:002012-03-18T22:09:47.292-07:00Neil, great reminder! Independence between the la...Neil, great reminder! Independence between the lambda and the h is a very often overlooked assumption indeed.AlexGilgurhttps://www.blogger.com/profile/01961676712058514905noreply@blogger.comtag:blogger.com,1999:blog-6977755959349847093.post-27285453549526602582012-02-29T11:57:15.022-08:002012-02-29T11:57:15.022-08:00Added a new plot to explain the connection between...Added a new plot to explain the connection between <b>Little's law</b> (N, the average number in the system) and Unix/Linux <b>load-average data</b> represented by the usual time series one sees coming from modern performance monitoring tools.Neil Guntherhttps://www.blogger.com/profile/11441377418482735926noreply@blogger.com