This morning, while having breakfast (nice cup of coffee and a sandwich), it came to my mind the queueing theory (probably because yesterday, while driving to Valencia, I remembered one of the first chapters of Numb3rs, when Charlie uses this theory to explain a car accident).
Summarising, Little’s Law JUST (like if it was small talk) says is the average number of units in an stable system (when in the long-term), equals the long-term rate of arrival (gamma) times the long-term average time this unit spends on the system.
L = [gamma] x W
So, where else does my sandwich fits on this?. Don’t you know?: my mouth can taste on average that many units related to the speed and pace of bitting, drinking, swallowing… but only if eating a sandwich could be considered as a long-term activity…
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Here in Spain it’s usual that a part of the mass is what we call the ‘cepillo’ (donations). How much is the total ‘collection’?. If we assume no notes are handed over and we can’t sumise the coin value for its ‘clinck’, one of the possibilities we have in order to estimate the total collection is:
1) Count the number of coins based on the number of ‘clincks’.
Sup. 1 ‘clinck’ = 1 coin
2) Consider Benford’s Law to estimate the distribution of the coins.
|
Coin
Starts with
|
Probability
of occurence
|
| 1 |
30.1% |
| 2 |
17.6% |
| 3 |
12.5% |
| 4 |
9.7% |
| 5 |
7.9% |
| 6 |
6.7% |
| 7 |
5.8% |
| 8 |
5.1% |
| 9 |
4.6% |
Here in Europe we have coins of 1c, 2c, 5c, 10c, 20c, 50c, 1 EUR, 2 EUR. So, the previous table could be re-written (n.b.: guesstimation):
|
Coin
|
Probability
of occurence
|
|
1c, 10c, 1 EUR
(Simple Average = 37c)
|
54.1 % |
|
2c, 20c, 2 EUR
(Simple Average = 74c)
|
31.7 % |
|
5c, 50c
(Simple Average = 27.5c)
|
14.2 % |
Other possibility is to wait until the end of the fiscal year and expect your Parish will make available the collection figures and try to estimate a weighted average for a normal Sunday. And we’ll be having better information, since the method is quite flawed, starting for the distribution of coins in the pocket may follow a uniform distribution, plus the simple averages used in the second table don’t make any sense. However, this is a starting point.
Disclaimer: I attended a Catholic School, I even tutorised church lessons for two years while in High School; I’m very respectful to any religion, including Catholicism, whenever they are respectful to the rest. This was just an exercise of applying OR to another normal aspect of life.
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