tag:blogger.com,1999:blog-6977755959349847093.post6719975865244021192..comments2017-02-08T00:24:53.878-08:00Comments on The Pith of Performance: Little's Law and IO PerformanceNeil Guntherhttp://www.blogger.com/profile/11441377418482735926noreply@blogger.comBlogger11125tag:blogger.com,1999:blog-6977755959349847093.post-3784407822034851372012-09-27T03:56:56.434-07:002012-09-27T03:56:56.434-07:00Hi Dr. Gunther,
I realised that there is a connect...Hi Dr. Gunther,<br />I realised that there is a connection between Little law and warehouse management.<br />In particular it is known that the mean residence time of materials in a warehouse for a period is<br />S = mean numer of items in stock for the period / mean number of additional items in that period<br />mean numer of items in stock = (quantity in stock at period start + quantity in stock at period end)/2 -> (Qs + Qe)/2<br />mean number of additional items in that period = (number of items arrived + number of items departed)/2 -> (Ia + Id)/2<br /><br />S =((Qs + Qe)/2) / ((Ia + Id)/2) = (Qs + Qe)/(Ia + Id).<br /><br />In a steady state as per Little Law case we have Qs = Qe and Ia = Id, which semplify the equation above to<br />S=Q/I -> Q=I*S<br /><br />I wouldn't be surprised if Little Law was known by Romans which applied taxes on wheat production :-)<br />MatteoPMatteohttp://www.blogger.com/profile/04543214611852575232noreply@blogger.comtag:blogger.com,1999:blog-6977755959349847093.post-79507760980501815352012-09-17T11:49:45.173-07:002012-09-17T11:49:45.173-07:00I wasn't aware of this book or Palm Calculus. ...I wasn't aware of this book or Palm Calculus. I'll have to investigate, when I can find the time. Thanks for the reference.<br /><br />It's not too surprising that LL would arise as a special case, given its dimensional simplicity.<br />Neil Guntherhttp://www.blogger.com/profile/11441377418482735926noreply@blogger.comtag:blogger.com,1999:blog-6977755959349847093.post-59939527926485462272012-08-26T10:13:54.941-07:002012-08-26T10:13:54.941-07:00Are you familiar with the Palm Calculus and the re...Are you familiar with the Palm Calculus and the result known as 'kitchen sink theorem' proved in the mid 90s, of which Little's law is now known to be a special case, as well as numerous other signal processing results, such as campbell's relation for shot noise?<br /><br />http://perfeval.epfl.ch/ , ch. 7<br /><br />The fellow at the link uses it to analyze the performance of mobile phone networks in simulations.<br /><br />The {'time to event' x mean duration of event} relation shows up in other interesting places in the 'big data' world -- specifically, the top level relation of paid search advertising (Revenue per search = Cost per click x click rate) where money takes the place of time. ;)<br /><br />There is also a relation, much used by actuaries, the Wald Identity, that seems to me to have interesting connection to this topic. Specifically, it relates the time until the first large insurance claim and the time-average cost of claims. I think it works (in the sense of your books) because the first event is special, in the sense of the Commuter's paradox or P-K correction. That is, it encodes details of the CoV of the distribution. Thus if you now the expectation of its occurrence you know quite a bit besides just the average time to the next event.<br /><br />Anyway, I think a more modern treatment of Little's Law would at least allude to these connections. They come up in practical work, esp. as regards simulation techniques, actuarial work, and 'value at risk' sorts of calculations involving paid search advertising -- more general than computer performance in the narrow sense, but performance analysts get dragged into 'big data' these days, whether we like it or not!John Goodwinhttp://www.blogger.com/profile/00147578789638409836noreply@blogger.comtag:blogger.com,1999:blog-6977755959349847093.post-20597551428841205892012-08-09T11:10:55.140-07:002012-08-09T11:10:55.140-07:00Just added my presentation slides.Just added my presentation slides.Neil Guntherhttp://www.blogger.com/profile/11441377418482735926noreply@blogger.comtag:blogger.com,1999:blog-6977755959349847093.post-50756288218902454752012-08-05T12:25:58.443-07:002012-08-05T12:25:58.443-07:00Thought you'd never ask. All will be revealed ...Thought you'd never ask. All will be revealed on Tuesday. :)Neil Guntherhttp://www.blogger.com/profile/11441377418482735926noreply@blogger.comtag:blogger.com,1999:blog-6977755959349847093.post-49042218718800089612012-08-05T12:19:43.828-07:002012-08-05T12:19:43.828-07:00That's a pretty interesting plot you included ...That's a pretty interesting plot you included with your post. I assume R(s) means response time in seconds, X(QPS) is throughout expressed in queries per second, and N is number of users. <br /><br />What do the red and blue dots represent, and what's behind the color change as values increase?Kenhttp://www.blogger.com/profile/01740718358083717805noreply@blogger.comtag:blogger.com,1999:blog-6977755959349847093.post-63875314163529269572012-08-03T08:48:56.197-07:002012-08-03T08:48:56.197-07:00I'm doing research, rather than product dev, b...I'm doing research, rather than product dev, but this press release from yesterday would seem to be along the lines you're interested in.<br /><br /> PR: <a href="http://slashdot.org/topic/datacenter/fusion-ios-ion-shares-flash/" rel="nofollow">Fusion-io's ION software turns its ioMemory into a shared storage target</a>.Neil Guntherhttp://www.blogger.com/profile/11441377418482735926noreply@blogger.comtag:blogger.com,1999:blog-6977755959349847093.post-32519491119634135262012-08-02T11:03:24.756-07:002012-08-02T11:03:24.756-07:00Hopefully ncCMG will post the slides after the mee...Hopefully ncCMG will post the slides after the meeting. I just love the idea of 1B IOPS for a critical OLTP database like trading systems. Do you know if Fusion-io is working on techniques to provide storage-based replication like EMC SRDF for business continuity or disaster recovery?metasofthttp://www.blogger.com/profile/17149213781391733478noreply@blogger.comtag:blogger.com,1999:blog-6977755959349847093.post-41700111867813384702012-08-01T14:16:01.918-07:002012-08-01T14:16:01.918-07:00Not only wrong coast, but wrong pond. :) Though ra...Not only wrong coast, but wrong pond. :) Though rather near my Alma Mater (Soton).<br /><br />It's been a while since I gave a ncCMG presentation, but last time they certainly did not record the sessions.<br /><br />Maybe go and bang on <a href="http://www.ukcmg.org.uk/" rel="nofollow">UK-CMG</a> to get me over there, once the Olympics mob has cleared out. :)Neil Guntherhttp://www.blogger.com/profile/11441377418482735926noreply@blogger.comtag:blogger.com,1999:blog-6977755959349847093.post-45301023535121845922012-08-01T13:44:39.110-07:002012-08-01T13:44:39.110-07:00This comment has been removed by a blog administrator.gjlhttp://www.blogger.com/profile/03674881180431139945noreply@blogger.comtag:blogger.com,1999:blog-6977755959349847093.post-66125719396621620272012-08-01T13:43:58.420-07:002012-08-01T13:43:58.420-07:00I would be very interested in hearing what you hav...I would be very interested in hearing what you have to say on this topic - but I am on the wrong coast. Is there any chance of having the session recorded? Even if audio only?gjlhttp://www.blogger.com/profile/03674881180431139945noreply@blogger.com