Show one half the expected number of arrivals for process

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Reference no: EM13909402

(a) Let the inter-renewal interval of a renewal process have a second- order Erlang density, fX (x) = λ2x exp(-λx). Evaluate the Laplace transform of m(t) = E [N(t)].

(b) Use this to evaluate m(t) for t ≥ 0. Verify that your answer agrees with (5.59).

(c) Evaluate the slope of m(t) at t = 0 and explain why that slope is not surprising.

(d) View the renewals here as being the even numbered arrivals in a Poisson process of rate λ. Sketch m(t) for the process here and show one half the expected number of arrivals for the Poisson process on the same sketch. Explain the difference between the two.

Text Book: Stochastic Processes: Theory for Applications By Robert G. Gallager.

Reference no: EM13909402

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