Network Protocol Performance Bounding Exploiting Properties of Infinite Dimensional Linear Equations ⋆

Abstract. This paper presents a quite versatile and widely applicable performance analysis methodology that has been applied for the study of network resource allocation protocols in the past. It is based on the identification ofrenewal cycles of theoperation of thesystem andthe setting up of recursive equations with respect to quantities-indices defined over the renewal cycles and sessions that appear within. Application of the expectation operator on these equations leads to infinite dimensional systems of linear equations which are shown to posses certain properties leading to rigorous and almost arbitrarily tight bounds on various performance metrics of interest. The special case of a random access protocol is used as an example in order to illustrate the derivation of the recursive equations capturing the protocol dynamics and system inputs. Finally, some other examples of application of the methodology are briefly discussed, illustrating the versatility and powerfulness of the approach. This analysis methodology can be quite useful for understanding the behavior of current complex and large scale networking environments, as well as assessing their scalability, stability and performance.