A Hessenberg Markov chain for fast fibre delay line length optimization

Abstract

In this paper we present an approach to compute the invariant vector of the N + 1 state Markov chain P presented in (Rogiest et al., Lecture Notes in Computer Science, NET-COOP 2007 Special Issue, pp. 4465:185-194) to determine the loss rate of an FDL buffer consisting of N lines, by solving a related Hessenberg system (i.e., a Markov chain skip-free in one direction). This system is obtained by inserting additional time instants in the sample paths of P and allows us to compute the loss rate for various FDL lengths by solving a single system. This is shown to be especially effective in reducing the computation time of the heuristic LRA algorithm presented in (Lambert et al., Proc. NAEC 2005, pp. 545-555) to optimize the FDL lengths, where improvements of several orders of magnitude can be realized