Sizing tape libraries

Sizing tape libraries
By Tim Hare

There's a little bit of math, from queuing theory, that can help when sizing a tape library. It's called Little's Law and without going into the etailed math, basically what it says is that the total number of items in a queuing system (L) is equal to the arrival rate (l) times the average waiting time, including the service time (W).

L = lW

This can be used to show why a slow teller causes lines to form at the bank, for example. But, if for a tape library, you say the arrival rate is the number of tapes created per day, and the service time is the number of days you keep that tape, then the number of tapes you need is the product of these two. For example, if you create three tapes per day that have to be retained for a week, then you need 21 tapes to handle that. You also need 21 slots in your library if you want it to be totally automated. This gives a good ballpark number, although you do have to do some rounding up because in practice, fractional tapes aren't used.

If you have several different kinds of backups or other tape needs, do the formula for each different kind, and sum the results - time periods all need to be the same though:

1 tape per week incremental with retention of 6 days = 1/7 per day X 6 days = 6/7 of a tape
1 tape per week incremental with retention of 5 days = 1/7 X 5 = 5/7 of a tape
1 tape per week incremental with retention of 4 days = 1/7 X 4 = 4/7 of a tape

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1 tape per week incremental with retention of 3 days = 1/7 X 3 = 3/7
1 tape per week incremental with retention of 2 days = 1/7 X 2 = 2/7
1 tape per week incremental with retention of 1 days = 1/7
1 tape per week full backup with retention of 7 days = 1/7 X 7 = 1 tape

The total of all this, if you add it up, is four tapes. But in actual practice, you would round up to one tape for each of the incrementals; therefore, you would end up with seven tapes needed.

This was first published in July 2001

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