On the continued Erlang loss function (Q1077826)

Results: 1) The continuation \(B(x,a)=\{a\int^{\infty}_{0}e^{- at}(1+t)^ xdt\},\) \(a>0\), \(x\geq 0\), of the Erlang loss function is convex. 2) For given mean \(\mu\geq 0\) and peakedness factor \(\zeta\geq 1\) there exist exactly one pair (a,x), \(a>0\), \(x\geq 0\), such that the continuations of the mean function m(x,a) and the peakedness function z(x,a) of the overflow process of the associated Erlang system coincide with \(\mu\) and \(\zeta\).