6. Consider a renewal process {N(t), t 0} having a gamma (r, ) interarrival distribution. That is,...

6. Consider a renewal process {N(t), t 0} having a gamma (r, λ) interarrival distribution.

That is, the interarrival density is

where [i/r] is the largest integer less than or equal to i/r.
Hint: Use the relationship between the gamma (r, λ) distribution and the sum of r independent exponentials with rate λ to define N(t) in terms of a Poisson process with rate λ.

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f(x) = e-xx(xx)-1 (r-1)! x>0 (a) Show that P[N(t) > n} = (t) i=nr (b) Show that m(t) = e-e (ht) i!