Renewal Model of a Buffered Optical Burst Switch

Optical Engineering, 2009

An enhanced mathematical model is introduced to study and evaluate the performance of a core node in an optical burst switched network. In the proposed model, the exact Poisson traffic arrivals to the optical burst switching ͑OBS͒ node is approximated by assuming that the maximum allowed number of arrivals to the OBS node, in a given time slot, is 2 ͑instead of ϱ͒. A detailed state diagram is outlined to illustrate the problem, and then a mathematical model based on the equilibrium point analysis technique is presented. Two performance measures, namely, the steady-state system throughput and the average blocking probability, are derived from the model, which is built in the absence of wavelength conversion capability. Our proposed model is aided by a simulation work that studies the performance of an OBS core node under the assumption of Poisson traffic arrivals ͑the exact case͒ and calculates the steady-state system throughput. The results obtained from the proposed mathematical model are consistent with that of simulation when assuming Poisson traffic arrivals, and this consistency holds for a certain range of traffic load. The effect of varying different network parameters on the average blocking probability is discussed.

Optical buffers based on Fiber Delay Lines (FDL) have been proposed for contention resolution in optical packet/burst switching systems. In this article, we propose a retrial queuing model for FDL optical buffers in asynchronous optical switching nodes. In the considered system, the reservation model employed is of post-reservation type and optical packets are allowed to re-circulate over the FDLs in a probabilistic manner. We combine the MMPP-based overflow traffic models of the classical circuit switching literature and fixed-point iterations to devise an algorithmic procedure to accurately estimate blocking probabilities as a function of various buffer parameters in the system when packet arrivals are Poisson and packet lengths are exponentially distributed. The proposed algorithm is both accurate and fast, allowing one to use the procedure to dimension optical buffers in next-generation optical packet switching systems.

IEEE Journal on Selected Areas in Communications, 2006

In this paper, we study the blocking probabilities in a wavelength division multiplexing-based asynchronous bufferless optical packet/burst switch equipped with a bank of tuneable wavelength converters dedicated to each output fiber line. Wavelength converter sharing, also referred to as partial wavelength conversion, corresponds to the case of a number of converters shared amongst a larger number of wavelength channels. In this study, we present a probabilistic framework for exactly calculating the packet blocking probabilities for optical packet/burst switching systems utilizing wavelength converter sharing. In our model, packet arrivals at the optical switch are first assumed to be Poisson and later generalized to the more general Markovian arrival process to cope with very general traffic patterns whereas packet lengths are assumed to be exponentially distributed. As opposed to the existing literature based on approximations and/or simulations, we formulate the problem as one of finding the steady-state solution of a continuous-time Markov chain with a block tridiagonal infinitesimal generator. To find such solutions, we propose a numerically efficient and stable algorithm based on block tridiagonal LU factorizations. We show that exact blocking probabilities can be efficiently calculated even for very large systems and rare blocking probabilities, e.g., systems with 256 wavelengths per fiber and blocking probabilities in the order of 10 −40. Relying on the stability and speed of the proposed algorithm, we also provide a means of provisioning wavelength channels and converters in optical packet/burst switching systems.

We propose an approximate analytic model of a multi-port optical burst switch equipped with fibre delay lines for non-Poisson arrivals. The analysis is formulated in terms of virtual traffic flows from which we derive expressions for the burst blocking probability. We simplify the analysis characterising the traffic flows by the mean and the variance of the channel occupancy distribution. The method is validated through comparison with results from a discrete-event simulator.

… (ICT), 2010

A mathematical model is introduced for performance evaluation of an OBS core node employing either no or full wavelength conversion strategies. Furthermore, the model assumes long-range dependent (LRD) traffic arrivals to the OBS intermediate node which are accurately modeled by Pareto distribution. In our proposed model, each output port is imitated by a GI/M/w/w queue for which a single performance measure; namely the burst loss probability, is evaluated from the model equations. Also, results of this model are compared with those obtained while assuming short-range dependent (SRD) Poisson arrivals to the core node in the two cases of no and full wavelength conversion. Finally, results show that traditional Poisson traffic models yields over-optimistic performance measures in terms of lower burst loss probability when compared to the more accurate long-range dependent Pareto traffic model. This discrepancy between the two models is much clearer for light traffic scenarios due to the more significant impact of self-similarity.

2011 IEEE Symposium on Computers and Communications (ISCC), 2011

We propose an approximate modelling method for analysing networks of optical burst switches with shared fibre delay lines (FDLs). To achieve a good accuracy in evaluating burst loss probabilities in the network, and allow a tractable solution method, a two-moment analysis is applied, both to traffic flows within network nodes and on network links. We believe the method is useful for evaluating the performance of shareper-node buffer architectures, which are generally more costefficient in terms of switching hardware requirements. Results show good accuracy compared to discrete-event simulations.

Lecture Notes in Computer Science, 2008

In Optical Burst-Switched networks, the so-called Burst-Control Packet is sent a given offset-time ahead of the optical data burst to advertise the imminent burst arrival, and reserve a time-slot at each intermediate node to allocate the incoming optical burst. This work proposes a methodology to estimate the number of packets to arrive in a given amount of time, in order to make it possible to send the BCP packet straightafter the first packet arrival and reduce the latency experienced during the burst-assembly process. The following studies the impact of a wrong guess in terms of overreservation of resources and waiting-time at the assembler, providing a detailed characterisation of their probability density functions. Additionally, a case example in a scenario with non-homogeneous Poisson arrivals is analysed and it is shown how to choose the appropriate burst-assembly algorithm values to never exceed a given over-reservation amount.

… IEEE GLOBECOM 2008 …, 2008

An enhanced mathematical model is introdu evaluate the performance of a core node in switched network. In the proposed model, t traffic arrivals to the OBS node is approxim that the maximum allowed number of arrivals in a given time slot, is two (instead of infinity) diagram is outlined to illustrate the probl mathematical model based on the equilibriu (EPA) technique is presented. The ste throughput is derived from the model whic absence of wavelength conversion capability model is aided by a simulation work w performance of an OBS core node under t Poisson traffic arrivals (the exact case) and calc state system throughput. The results obtained f mathematical model are consistent with that o assuming Poisson traffic arrivals and this consi wide range of traffic load.

Performance Evaluation, 2009

Novel switching approaches like Optical Burst/Packet Switching have buffering implemented with Fiber Delay Lines (FDLs). Previous performance models of the resulting buffer only allowed for solution by numerical means, and only for one time setting: continuous, or discrete.

Elsevier Computer Communications, 2010

Optical Burst Switching (OBS) has been widely admitted as a viable candidate for the evolving all-optical network control framework of nowadays Internet core to meet the explosive demand of bandwidth constraints in multimedia and real-time applications. A number of analytical models have been proposed to characterize the behavior of OBS networks. These models, however, do not imitate the actual features of the Fiber Delay Line (FDL) components present in contemporary optical switches. Underscoring the precise behavior of FDLs leads to misleading results regarding major performance measures of OBS networks. While FDLs behavior has been neglected in many studies, as a crude approximation, a few researches characterize FDLs as conventional buffers present in electronic switching systems. In this paper, we provide an inclusive discussion on the features of FDLs, followed by presenting a novel analytical model to realize the inimitable characteristics of FDLs. The proposed network-level model is based on the results of queuing systems with impatient customers and deterministic impatience time. The viability of the proposed model is validated through extensive simulation experiments.