Introduction to numerical analysis: 2nd edition
Introduction to numerical analysis: 2nd edition
SIAM Journal on Scientific and Statistical Computing
Warranty cost analysis for nonrepairable services products
International Journal of Systems Science
Contention in multi-hop wireless networks: model and fairness analysis
Proceedings of the 12th ACM international conference on Modeling, analysis and simulation of wireless and mobile systems
The effect of contention in CSMA networks: Model and fairness protocol
Performance Evaluation
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The integral equation of renewal type has many applications in applied probability. However, it is rarely solvable in closed form. In this paper, we describe a numerical method for finding approximate solutions to integral equations of renewal type based on quadrature rules for Stieltjes integrals previously developed by the author. We provide error analyses for our numerical solution based on the trapezoid-like rule for Stieltjes integrals and describe computational experience with two solution algorithms based on the trapezoid-like and the Simpson-like rules for Stieltjes integrals. We discuss a link between discrete and continuous renewal theory that is illuminated by the numerical solution method. The proposed numerical method is simple, amenable to direct error analysis, performs better than previously proposed approximations in many cases of significant practical interest, and is capable of handling some cases on which other methods fail.