Past exam of the mathematics course of the University of Cambridge / 2007 / ii / Paper 1 / 26J / a

Solution

Write the successive gaps of the rate-

λ

E_{j}

. The first arrivals in the three streams occur at

E_{1}

E_{1} + E_{2}

, and

E_{1} + E_{2} + E_{3}

. They have Erlang distributions of shapes one, two and three:

f_{i} (t) = \frac{λ ^{i} t ^{i - 1} e ^{- λ t}}{( i - 1 )!}, t \geq 0, i = 1, 2, 3.

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