The following information was submitted:
Transactions: WSEAS TRANSACTIONS ON MATHEMATICS
Transactions ID Number: 29-350
Full Name: Jorge Sá Esteves
Position: Assistant Professor
Age: ON
Sex: Male
Address: Dep. Mathematics, University of Aveiro, 3810-193 AVEIRO
Country: PORTUGAL
Tel: 234323962
Tel prefix: 351
Fax: 234370066
E-mail address: saesteves@ua.pt
Other E-mails: jsaesteves@netcabo.pt
Title of the Paper: efficient algorithms for higher-order derivatives of the continued erlang delay function
Authors as they appear in the Paper: Jorge Sá Esteves
Email addresses of all the authors: saesteves@ua.pt
Number of paper pages: 11
Abstract: 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 derivatives. For comparison purposes, it is also generalized a numerical method based on a quadrature procedure suggested by D. L. Jagerman~\cite{Jagr:87}. All the computational methods are compared in terms of stability, efficiency and precision. Our study concludes that a recursive matrix relation presented in a previous work~\cite{Este:95,Este:97}, may be used for the establishment of a simple and reliable algorithm having the best performance considering the trade-off of the different criteria. Extensive computational results are presented and discussed. In the sequel, a conjecture about the strict convexity o!
f the first derivative of Erlang delay function is presented and supported by numerical evidence.
Keywords: Performance Evaluation, Queueing Systems, Erlang's B and C Formulas, Numerical Differentiation.
EXTENSION of the file: .pdf
Special (Invited) Session: Algorithms for higher-order derivatives of Erlang C function
Organizer of the Session: 620-360
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