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This paper presents in a unified manner mathematical properties of the second order derivatives of the overflow traffic from an Erlang loss system, assuming the number of circuits to be a nonnegative real value. It is shown that the overflow traffic function Â(a, x) is strictly convex with respect to x (number of circuits), with x ≥ 0, taking the offered… (More)

- JORGE SÁ ESTEVES
- 2009

In this paper we analyze the partial derivatives of any order of the continued Erlang C function in the number of servers. For the numerical computation of those derivatives, several algorithms are proposed and compared in terms of stability, efficiency and precision. This study concludes that a recursive matrix relation presented in a previous work [4, 5],… (More)

- JORGE SÁ ESTEVES
- 2009

In this paper we analyze the partial derivatives of any order of the continued Erlang delay function in the number of servers. Several properties with strong analytical relations between the high-order derivatives of Erlang’s B and C functions are established. Using these relations, three algorithms are proposed for the numerical computation of the cited… (More)

- Jorge Sá Esteves, José M. F. Craveirinha
- J. Computational Applied Mathematics
- 2013

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