Talk:Little's law
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[edit] Early discussion
the corresponding article on h2g2 (by u129960) is mine. I have the relevant rights. Martin
Is there somthing usefull to retrieve from this article: JDC Little? Looxix 20:42 May 5, 2003 (UTC)
I removed the weird purple box as it looked inconsistent with other pages and I didn't want to start a precedent where everyone starts adding odd HTML to pages in order to produce features that don't add anything to the article. Angela 02:13, Sep 22, 2003 (UTC) (in an anti-html mood).
What is an "OAP" (referred to in this entry)?
OAP stands for Old Age Pensioner Tango
After seeing the query written into this article (not just on the talk page) I searched on Google and found that in Britain the term is frequently used to refer to old people. Not just pensioners, even if that's the etymology. What I saw on Google did not suggest what the letters stand for, and I remained ignorant until I saw Tango's answer above. OAP is regional dialect, not standard English. Michael Hardy 23:27, 8 Oct 2003 (UTC)
All "old people" in england are pensioners, because everyone over 60/65 is entitled to a state pension (some will correct me if i'm wrong), so it the meaning is the same whatever way you look at it. OAP is used across England (and the rest of the UK to the best of my knowledge), so doesn't that make it standard english? (standard english being that which is spoken in england, or so i thought). -- Tango
- No -- over the last few centuries English has become international. Many regional variations exist and England, like all other places where English is spoken, has usages that are only local (in some cases used throughout all of Britain and Ireland but not elsewhere, for example, and in some cases used only in the southern part of one county or the like) or ephemeral. England has imported lots of usages from France that have replaced more traditional English usages that remain standard in America ("6 September" instead of the traditional "September 6th", and lots of others) so that current American usage and Samuel Johnson's 18th-century usage may coincide where 21st-century British usage has been Frenchified or otherwise changed (e.g., the British no longer often use "gotten" as the past participle of "got"; Americans still do). I would say it would have to be more international and less ephemeral than "OAP" before I would call it "standard English". Michael Hardy 22:16, 11 Oct 2003 (UTC)
The claim about the counter and Little's law not applying in the previous version of this article was simply untrue. There is no requirement for arrivals to be independent in Little's Theorem. I have added a section which formalises things a bit and puts in the requirements for Little's Theorem to hold. I have removed incorrect claims about independent arrivals. --Richard Clegg 15:59, 15 Feb 2005 (UTC)
- Given this, and that there have been no complaints about accuracy posted here in at least two years (going by the timestamp of your comment), is there any need to keep the dispute box on the article? Ubernostrum 08:29, 20 June 2007 (UTC)
"The only requirement is that the system is stable -- it can't be in some transition state such as just starting up or just shutting down." This is false, no? —Preceding unsigned comment added by 128.83.52.232 (talk) 18:17, June 7, 2007
- No, because in the transition state assumptions about stable rates of arrival and/or time in the system don't hold. At startup, for example, when the system is empty, the rate of arrival may be much higher than in stable operation, as the system fills to capacity. Or, at shutdown, the time spent in the system may be much lower than in stable operation because the system must clear itself out prior to shutting down. Ubernostrum 07:42, 20 June 2007 (UTC)
- Additionally, at shutdown, the rate of arrival will drop to zero since, at some point, the system must stop accepting new clients. Ubernostrum 08:27, 20 June 2007 (UTC)
Yes, I agree with you on these two points, so maybe I should be more clear. From the sentence I quoted, the implication seems to be that stability and not being in a transition state are equivalent. Trivially I can have a system with a higher rate of input than output, not be in a transition state, yet the queue would be unstable. Perhaps all that is needed is a rewording to remove the implied equivalence of the two parts of the sentence.
- Perhaps the problem is with differing senses of the word "stable"; if you feel that the current wording may cause confusion, fix it ;) Ubernostrum 08:46, 5 July 2007 (UTC)
The article states that the only requirement of the system is that it operates on a FCFS basis. AFAICT this is completely wrong. The only requirement is the stationary property of the system. Wppds 13:51, 16 August 2007 (UTC)
- After looking further into it I think the theorem holds for all work-conserving dequeuing disciplines. Or it least it holds for this more general property. If nobody objects I will change it to state this in the abstract. Wppds 17:50, 20 August 2007 (UTC)
- I full agree with Wppds's statement. BusaJD 14:12, 6 September 2007 (UTC)
- I completely agree, the original publication states (discussion section, page 5): "The results are remarkably free of specific assumptions about arrival and service distributions, independence of interarrival times, number of channels, queue discipline, etc. A requirement is made for strict stationarity (although this is probably not the weakest requirement possible), but the steady state in most current queuing models would appear to be strictly stationary. Similarly, in cases of practical interest, the arrival process is likely to be metrically transitive." 128.105.181.38 (talk) 19:48, 14 December 2007 (UTC)
From the article:
- Let α(t) be the arrival rate to some system in the interval [0, t]. Let β(t) be the number of departures from the same system in the interval [0, t]. Both α(t) and β(t) are integer valued increasing functions by their definition.
I don't see how this is true. If α(t) is really the arrival rate, then how is it an increasing function? I see the definition being α(t) = p / t, where p is the number of things that have entered the queue. This is not gauranteed to be increasing. I can think of a few trivial counterexamples if someone needs proof. 157.130.62.194 (talk) 14:37, 22 January 2008 (UTC)
- The arrival rate can, and is often assumed as, an exponential function. An exponential function, say, f(x)=e^x, is a valid example of an increasing function. Lucky boi (talk) 02:16, 25 January 2008 (UTC)
- Alright, by this I must have defined α(t) incorrectly. Using the definition above, we take example of people arriving in a store. Let's assume that it's black friday and the store is open for 8 hours and there are 100 people waiting outside for their new Wii's. In the first hour, 100 people arrive in the store, buy the Wiis and the store sells out. On news of this, no new people enter the store. Then α(1) = 100 people/hour, and α(8) = 100/8 = 14.5 people/hour. This is not increasing. Now if we take &alpha(t) to be the gross amount of people that visited, I can see how it is a non-decreasing function. It would appear to me to usually be linear though, I'd love to see the justification for exponential though. —Preceding unsigned comment added by 12.189.106.194 (talk) 07:39, 25 January 2008 (UTC)
Mathematical Formalization
We should take this section out. It isn't correct, as I illustrated above, and it's a gross simplification of the real proof. If someone wants the proof, they can find it. It is neither general enough to express in English, nor well defined enough to really be saying anything. I'll look at this tomorrow and decide weather it's worth cleaning up or deleting completely.12.189.106.194 (talk) 08:29, 25 January 2008 (UTC)
74.244.85.252 (talk) 07:25, 13 February 2008 (UTC)I made some simple edits (stressing long-term). This is how I explain it to students when I am teaching queueing theory.
