Algorithms for higher-order derivatives of Erlang C function

Authors:
Jorge Sá Esteves
Affiliations:
University of Aveiro, Department of Mathematics, Aveiro, Portugal
Venue:
ICCOM Proceedings of the 13th WSEAS international conference on Communications
Year:
2009

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Abstract

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], may be used for the establishment of a simple and reliable algorithm having the best performance considering the trade-off of the different criteria. Some computational results are presented and discussed. A conjecture about the convexity of the first derivative is supported by these computational results.