Comments on a paper by A. J. Branford Branford [1] states and proves that the overflow process from an N -state birth-death process is a renewal process with inter-event times characterized by a hyperexponential distribution with N components. The same result and a similar proof were published earlier in [3] . The proof in [3] is in fact somewhat shorter since use was made of Chihara's important result ([2], Theorem 1.9.1 and Corollary) that a sequence of polynomials defined by a recurrence relation of the form