A Hessenberg Markov chain for fast fibre delay line length optimization

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

A Performance Model for an Asynchronous Optical Buffer 1

We investigate the behaviour of an asynchronous optical buffer by means of a continuous-time queueing model. Through a limit procedure, previously obtained results for a discrete-time queueing model are translated to a continuous-time setting. We also show that the same results can be obtained by a direct analysis using Laplace transforms. Closed-form expressions are obtained for the cases of exponentially distributed burst sizes, deterministic burst sizes and mixtures of deterministic burst sizes. The performance of asynchronous optical buffers shows the same characteristics as that of synchronous optical buffers: a reduction in throughput due to the creation of voids on the outgoing channel and a burst loss probability that is strongly influenced by the choice of fiber delay line granularity. The optimal value of the latter depends on the burst size distribution and the offered load

Analysing queueing behaviour in void-avoiding fibre-loop optical buffers

In optical packet/burst switching, fibre-loop optical buffers provide a compact and effective means of contention resolution. In case of a fixed packet length, the involved loop length is typically chosen matched (equal to the packet length), and the loops are arranged in parallel, constituting a single-stage buffer. In this contribution, we investigate the performance of such a buffer in an asynchronous network setting, assuming (batch-)Poisson arrivals and assuming a so-called void-avoiding schedule (VAS). We show that by time discretisation, the fibre-loop system behaviour can be captured by a particular type of exhaustive polling model. Performance measures such as the moments of the queue content and packet delay for the discretised as well as for the asynchronous optical buffer model are obtained. We illustrate our approach by various numerical examples obtain several insights, including the contra-intuitive finding that under the VAS, both the standard deviation and the coefficient of variation of the queue content are lower than under other regular scheduling disciplines

Analysis of an asynchronous single-wavelength FDL buffer. Accepted for Publication

Abstract. We investigate the behaviour of an asynchronous single-wavelength fiber delay line (FDL) buffer by means of a continuous-time queueing model. Through a limit procedure, previously obtained results for a discrete-time queueing model are translated to a continuous-time setting. The two important cases of exponentially distributed burst sizes and deterministic burst sizes are discussed in detail. The performance of asynchronous optical buffers proofs to be similar to that of synchronous optical buffers: a reduction in throughput due to the creation of voids on the outgoing channel and a burst loss probability that is strongly influenced by the choice of FDL granularity. The optimal value of the latter depends on the burst size distribution and the offered load. Synchronisation is found to be advantageous, yielding a lower loss than the asynchronous case for the same offered load