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| In [[queueing theory]], a discipline within the mathematical [[probability theory|theory of probability]], '''Little's result''', '''theorem''', '''lemma''', '''law''' or '''formula'''<ref>{{cite book|title=Probability, statistics, and random processes for electrical engineering|author=Alberto Leon-Garcia|publisher=Prentice Hall|year=2008|edition=3rd|isbn=0-13-147122-8}}</ref><ref name="allen">{{cite book | page = 259 | title = Probability, Statistics, and Queueing Theory: With Computer Science Applications | first = Arnold A. | last = Allen | publisher = Gulf Professional Publishing | year = 1990 | isbn = 0120510510}}</ref> is a theorem by [[John Little (academic)|John Little]] which states:
| | Have we been thinking "how do I speed up my computer" lately? Well odds are when you are reading this article; then we may be experiencing one of many computer issues which thousands of people discover that they face on a regular basis.<br><br>Install an anti-virus software. If you absolutely have which on we computer then carry out a full program scan. If it finds any viruses found on the computer, delete those. Viruses invade the computer plus create it slower. To safeguard the computer from various viruses, it's greater to keep the anti-virus software running when you utilize the internet. You could additionally fix the safety settings of the internet browser. It usually block unknown plus dangerous websites and also block off any spyware or malware striving to get into a computer.<br><br>H/w associated error handling - whenever hardware causes BSOD installing newest fixes for the hardware and/ or motherboard could assist. We can additionally add new hardware which is compatible with the system.<br><br>The issue with many of the folks is that they do not wish To invest income. In the cracked adaptation 1 refuses to have to pay anything plus could download it from web easily. It is easy to install also. But, the problem comes whenever it happens to be unable to identify all possible viruses, spyware and malware inside the program. This really is considering it really is obsolete inside nature and does not get any regular updates from the website downloaded. Thus, your program is accessible to issues like hacking.<br><br>Another usual cause of PC slow down is a corrupt registry. The registry is a important component of computers running on Windows platform. When this gets corrupted the PC will slowdown, or worse, not start at all. Fixing the registry is simple with the employ of the system plus [http://bestregistrycleanerfix.com registry cleaner].<br><br>Active X controls are used over the whole spectrum of computer plus internet technologies. These controls are referred to as the building blocks of the web and as the glue which puts it all together. It is a standard that is utilized by all developers to create the web more helpful and interactive. Without these control standards there would basically be no public internet.<br><br>As the hub center of the computer, the important settings are stored the registry. Registry is structured because keys plus every key relates to a system. The program reads the keys plus utilizes the information to launch and run programs. However, the big issue is that there are too various unwelcome settings, useless information occuping the useful space. It makes the system run slowly and huge amounts of settings become unreadable.<br><br>Registry products could assist a computer run in a better mode. Registry cleaners must be piece of the standard scheduled repair program for the computer. You don't have to wait forever for your computer or the programs to load and run. A small maintenance may bring back the speed we lost. |
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| :The long-term average number of customers in a stable system ''L'' is equal to the long-term average effective arrival rate, ''λ'', multiplied by the ([[Palm calculus|Palm]]‑)average time a customer spends in the system, ''W''; or expressed algebraically: ''L'' = ''λW''.
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| Although it looks intuitively reasonable, it is quite a remarkable result, as the relationship is "not influenced by the arrival process distribution, the service distribution, the service order, or practically anything else."<ref>{{cite doi|10.1287/opre.1110.0941}}</ref>
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| The result applies to any system, and particularly, it applies to systems within systems.<ref>{{cite doi|10.1007/978-1-4612-1482-3_5}}</ref> So in a bank, the customer line might be one subsystem, and each of the tellers another subsystem, and Little's result could be applied to each one, as well as the whole thing. The only requirements are that the system is stable and non-preemptive; this rules out transition states such as initial startup or shutdown.
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| In some cases it is possible to mathematically relate not only the ''average'' number in the system to the ''average'' wait but relate the entire ''probability distribution'' (and moments) of the number in the system to the wait.<ref>{{cite doi|10.1016/0167-6377(88)90035-1}}</ref>
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| ==History==
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| In a 1954 paper Little's law was assumed true and used without proof.<ref name="little-graves">{{cite doi|10.1007/978-0-387-73699-0_5}}</ref><ref>{{cite doi|10.1287/opre.2.1.70}}</ref> The form L = λW was first published by [[Philip M. Morse]] where he challenged readers to find a situation where the relationship did not hold.<ref name="little-graves" /><ref>{{cite book | title = Queues, inventories, and maintenance: the analysis of operational system with variable demand and supply | first = Philip M. | last = Morse | authorlink = Philip M. Morse | publisher= Wiley | year = 1958 }}</ref> Little published in 1961 his proof of the law, showing that no such situation existed.<ref>{{cite doi|10.1287/opre.9.3.383}}</ref> Little's proof was followed by a simpler version by Jewell<ref>{{cite jstor|168616}}</ref> and another by Eilon.<ref>{{cite jstor|168368}}</ref> Shaler Stidham published a different and more intuitive proof in 1972.<ref>{{cite doi|10.1287/opre.22.2.417}}</ref><ref>{{cite doi|10.1287/opre.20.6.1115}}</ref>
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| ==Example==
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| Imagine a small store with a single counter and an area for browsing, where only one person can be at the counter at a time, and no one leaves without buying something. So the system is roughly:
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| ::''Entrance → Browsing → Counter → Exit''
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| In a stable system, the rate at which people enter the store is the rate at which they arrive at the store (called the arrival rate), and the rate at which they exit as well (called the exit rate). By contrast, an arrival rate exceeding an exit rate would represent an unstable system, where the number of waiting customers in the store will gradually increase towards infinity.
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| Little's Law tells us that the average number of customers in the store ''L'', is the effective arrival rate λ, times the average time that a customer spends in the store ''W'', or simply:
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| : <math>L = \lambda W \, </math>
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| Assume customers arrive at the rate of 10 per hour and stay an average of 0.5 hour. This means we should find the average number of customers in the store at any time to be 5.
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| : <math>L = 10 \cdot 0.5 = 5 </math>
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| Now suppose the store is considering doing more advertising to raise the arrival rate to 20 per hour. The store must either be prepared to host an average of 10 occupants or must reduce the time each customer spends in the store to 0.25 hour. The store might achieve the latter by ringing up the bill faster or by adding more counters.
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| We can apply Little's Law to systems within the store. For example, the counter and its queue. Assume we notice that there are on average 2 customers in the queue and at the counter. We know the arrival rate is 10 per hour, so customers must be spending 0.2 hours on average checking out.
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| : <math>W =\frac{L}{\lambda} = \frac{2}{10} = 0.2 </math>
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| We can even apply Little's Law to the counter itself. The average number of people at the counter would be in the range (0, 1) since no more than one person can be at the counter at a time. In that case, the average number of people at the counter is also known as the utilisation of the counter.
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| However, because a store in reality generally has a limited amount of space, it cannot become unstable. Even if the arrival rate is much greater than the exit rate, the store will eventually start to overflow, and thus any new arriving customers will simply be rejected (and forced to go somewhere else or try again later) until there is once again free space available in the store. This is also the difference between the ''arrival rate'' and the ''effective arrival rate'', where the arrival rate roughly corresponds to the rate at which customers arrive at the store, whereas the effective arrival rate corresponds to the rate at which customers ''enter'' the store. However, in a system with an infinite size and no loss, the two are equal.
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| ==Estimating parameters==
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| To use Little's law on data formulas must be used to estimate the parameters as the result does not necessarily directly apply over finite time intervals, due to problems like how to log customers already present at the start of the logging interval and those who have not yet departed when logging stops.<ref>{{cite doi|10.1287/opre.2013.1193}}</ref>
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| ==Applications==
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| Software-performance testers have used Little's law to ensure that the observed performance results are not due to bottlenecks imposed by the testing apparatus. See:
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| * [http://www.onjava.com/pub/a/onjava/2005/01/19/j2ee-bottlenecks.html Software Infrastructure Bottlenecks in J2EE by Deepak Goel]
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| * [http://arxiv.org/abs/cs/0404043 Benchmarking Blunders and Things That Go Bump in the Night by Neil Gunther]
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| Other applications include staffing emergency departments in hospitals.<ref name="50aniv">{{cite doi|10.1287/opre.1110.0940}}</ref><ref>{{cite web | url =http://www.epmonthly.com/subspecialties/management/littles-law-the-science-behind-proper-staffing/ | title = Little’s Law: The Science Behind Proper Staffing | first = Mark | last = Harris | date = February 22, 2010 | accessdate = September 4, 2012 | publisher = Emergency Physicians Monthly}}</ref>
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| ==See also==
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| * [[List of eponymous laws]] (laws, adages, and other succinct observations or predictions named after persons)
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| ==Notes==
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| {{reflist}}
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| ==External links==
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| *''[http://www.columbia.edu/~ks20/stochastic-I/stochastic-I-LL.pdf A Proof of the Queueing Formula L = λ W]'', Sigman, K., Columbia University
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| {{Queueing theory}}
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| [[Category:Operations research]]
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| [[Category:Queueing theory]]
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| [[fr:Loi de Little]]
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Have we been thinking "how do I speed up my computer" lately? Well odds are when you are reading this article; then we may be experiencing one of many computer issues which thousands of people discover that they face on a regular basis.
Install an anti-virus software. If you absolutely have which on we computer then carry out a full program scan. If it finds any viruses found on the computer, delete those. Viruses invade the computer plus create it slower. To safeguard the computer from various viruses, it's greater to keep the anti-virus software running when you utilize the internet. You could additionally fix the safety settings of the internet browser. It usually block unknown plus dangerous websites and also block off any spyware or malware striving to get into a computer.
H/w associated error handling - whenever hardware causes BSOD installing newest fixes for the hardware and/ or motherboard could assist. We can additionally add new hardware which is compatible with the system.
The issue with many of the folks is that they do not wish To invest income. In the cracked adaptation 1 refuses to have to pay anything plus could download it from web easily. It is easy to install also. But, the problem comes whenever it happens to be unable to identify all possible viruses, spyware and malware inside the program. This really is considering it really is obsolete inside nature and does not get any regular updates from the website downloaded. Thus, your program is accessible to issues like hacking.
Another usual cause of PC slow down is a corrupt registry. The registry is a important component of computers running on Windows platform. When this gets corrupted the PC will slowdown, or worse, not start at all. Fixing the registry is simple with the employ of the system plus registry cleaner.
Active X controls are used over the whole spectrum of computer plus internet technologies. These controls are referred to as the building blocks of the web and as the glue which puts it all together. It is a standard that is utilized by all developers to create the web more helpful and interactive. Without these control standards there would basically be no public internet.
As the hub center of the computer, the important settings are stored the registry. Registry is structured because keys plus every key relates to a system. The program reads the keys plus utilizes the information to launch and run programs. However, the big issue is that there are too various unwelcome settings, useless information occuping the useful space. It makes the system run slowly and huge amounts of settings become unreadable.
Registry products could assist a computer run in a better mode. Registry cleaners must be piece of the standard scheduled repair program for the computer. You don't have to wait forever for your computer or the programs to load and run. A small maintenance may bring back the speed we lost.