B.S.T.J. Briefs: Proof of a Convexity Property of the Erlang B Formula

Consider Poisson traffic offered to a group of n trunks. Blocked calls are cleared, and call holding times are independent and identically distributed. In equilibrium, the call congestion is given by the wellknown Erlang B formula1 B(n, a) = n » ' k--O where a is the offered load in erlangs. We prove here that B{n, a) - B{n + 1, a)