Calculation of mean burst length

A burst of lost packets is defined as a sequence of consecutive packets, all of which are marked as lost. The burst starts when a packet is lost after one or more packets have not been lost. Thus, the probability of a burst length of one is being at the bad state and then going to the good state. This probability is α. Similarly, the probability of a burst length of two is the probability of being at the bad state, but coming to this state at the next run. This probability is (1 - α)α. Thus in general the probability of a burst length of k packets is to be at the bad state for k - 1 times and the next run to go to the good state, which is (1 - α)^(k--1)α.

The mean bust length B is then:

B = α + 2(1 - α)α + 3(1 - α)²α+4(l - α)³α + ...+ k(1 -α)^k-1α + ...

summing this series, leads to:

(E.2) 

Rearranging eqn. E.2 gives:

(E.3) 

and rearranging eqn. E.1 and substituting for α from eqn. E.3 gives:

(E.4)