Past exam of the mathematics course of the University of Cambridge / 2001 / iii / Paper 26 / 3 / b / Solution

In this bufferless queue, queue overflow is the eventThe Poisson moderate deviation principle therefore givesThe same infimum is obtained for $x\ge C$, so replacing $Q_L>C$ by $Q_L\ge C$ gives the same logarithmic exponent. Any integer rounding of the service rate of a queue changes the scaled threshold by a quantity tending to zero.