Excercises

Erlang induction step

Derive the formula:

$$\text{“}\mathrm{Exp}(\lambda )+\mathrm{Erlang}(\ell ,\lambda )\sim \mathrm{Erlang}(\ell +1,\lambda )\text{”}$$

Observation: By repeatedly applying the above formula, we see that:

$$\text{“}\stackrel{\ell \text{ terms}}{\overbrace{\mathrm{Exp}(\lambda )+\cdots +\mathrm{Exp}(\lambda )}}\sim \mathrm{Erlang}(\ell ,\lambda )\text{”}$$