# data statistics converted to 15 minutes interval

I am trying to validate that the monthly bandwidth percent utilization with 60-minutes time interval is lower than the utilization with 15-minutes interval. Let say I have 20% bandwidth utilization at 12pm for 60-minutes interval. What will that be with 15-minute interval? Thanks
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Senior DeveloperCommented:
20% when there is no more information given and assuming a constant line speed.
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StatisticianCommented:
Hi there  leblanc,

If B is the bandwith fraction for a 60 minute period then the bandwidth fraction of a containing 15 minute period can be anything in the interval

[ (max(0, (4*B) - 3) .. min(1, 4*B) ]

(( If you think in percentages rather than fractions change the 1 and 3 into 100 and 300 respectively))

What that says is that

1. as long as the one hour bandwidth fraction is above 1/4 the 15 min bandwidth could reach 1 (or 100%)
2. as long as the one hour bandwidth fraction is below 3/4 the 15 min bandwidth could possibly be as low as 0.
That means that for the cases where the one hour bandwidth is between 1/4 and 3/4 the 15 min bandwith could possibly be anywhere between 0 and 1.  For cases below 1/4 and above 3/4 the possible values for 15 min bandwidth are restricted.

For your example of 1 hr bandwidth being 1/5 (or 20%) the range of possible bandwidth values for a containing 15 min interval is
[ 0 .. 4/5] (or 0 to 80%).

These results hold for both any nominated 60 minute interval as well as monthly averages for (say) the daily 12:00 -> 13:00 interval.

________

However it is most unlikely that you would have sharp difference in bandwidth consumption during a 60 minute period, and if the pattern of usage was absolutely constant then any 15 minute interval within the 60 minute would have identical bandwith usage values to the usage value for whole 60 minutes.

________

Then again it is possible for a critical piece of equipment to have failed within the 60 minute period, or alternately a radio station might broadcast competition website details producing a short sharp period of extremly heavy usage.  In both these cases the intervals above provide absolute limits which mathematically can't be exceeded.  That is, they allow for any and all possible situations.

________

If perchance you have unbiased historical values for 15 minutes bandwidth usage then you could construct likely confidence intervals to  go from 60 mins -> 15 mins which would be much shorter than those above.  However such analysis depends on

• prediction days/months being similar to past
• data from the past is unbiased
• recognising that confidence interval give a level of confidence that the true value is with the interval. Here confidence refers to the repeating the unbviased sampling excercise many times and stating the value is in the interval. The statement will be correct at least the nominated fraction of repeats.  Note that a confidence interval does not give probabilities - the value is either in the interval or not - it gives how confident we are of being correct.

Hope this is food for thought.

Ian
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AccountingAuthor Commented:
At the end, the bandwidth utilization is the same. If I have 20% based on the 60 minutes interval, it will be the same with the 5 minutes interval, except that the bandwidth utilization chart is more granular. Correct?
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StatisticianCommented:
No, well not in general.

That will only hold if utilisation is constant.

Consider bandwidth utilisation for a 24 hr period.  That may come out to be 15%.  But any particular 15 minute period could well be vastly different to the 15%.  The same argument holds when going from 1 hour to 15 minutes, though there usually is a smaller variation.  BUT a 15 minute period which is part of the 60 minute period (having 15% utilisation) could have a bandwidth utilisation value anywhere from 0% to 60%.

## To consider an analogy

If a car takes 1 hour 40 minutes to go 100 km it averages 60 km/hour.  That means if it went constant speed then that speed would be 60 km/hr.  However going though a crowded city the speed will be much lower and out in the country it might be going 100 km/hr or more.  In fact if there was a traffic jam in the city the car might be stopped for 15 minutes and then if it did  70.6  km/hr the rest of the way it would still end up with a 60 km/hr average.

So also with bandwidth usages.  The average rate doesn't necessarily apply to sub parts, though if each sub part has the same value then the whole will have that common value.
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