Two common properties of the erlang-B function, erlang-C function, and Engset blocking function

This paper develops two common properties of the Erlang-B function, Erlang-C function, and Engset blocking function. In analogy to the well-known recursion for computing the Erlang-B function, two recursions are constructed—one for computing the Erlang-C function and the other for computing the Engset blocking function. Based on these two common properties and the recursion, three algorithms are presented for each of the three functions.