Saturday, February 24, 2007

The problem of unit in the relationship between backorder and waiting time

The formula for the relationship between backorder and waiting time is
V[B]=lambda E[BW] + lambda^2 V[BW]

I think there is exact same formula in queueing theory about the number in the queue and waiting time. But the puzzle to me is the match of unit. Suppose the unit of B, lambda, BW are item, item/day, day. V[B]=item^2, lambda E[BW] = item and lambda^2 V[BW]=item^2.

If it was me to derive this formula, I would throw it into garbage after this check. But sometimes, we cannot trust common sense.

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