A Simple Algebraic Approximation to the Erlang Loss System

We use Palm calculus to derive a simple, intuitive system of two linear-quadratic equations and two unknowns, whose algebraic solution yields Harel's (1988) upper bound to the Erlang loss probability. We then derive a sequence of progressively stronger systems of equations, which eventually become exact. These algebraic relations provide a parsimonious, new metaphor for modeling Erlang loss behaviour within optimization models. We illustrate our framework using two example applications.

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