ABSTRACT Providing a photonic alternative to the current electronic switching in the backbone, op... more ABSTRACT Providing a photonic alternative to the current electronic switching in the backbone, optical packet switching (OPS) and optical burst switching (OBS) require optical buffering. Optical buffering exploits delays in long optical fibres; an optical buffer is ...
We present a performance model for fiber delay line (FDL) buffers having access to multiple wavel... more We present a performance model for fiber delay line (FDL) buffers having access to multiple wavelengths on an output fiber. In optical burst switching and optical packet switching, contending bursts (or packets) need to be dealt with in an effective way, and both wavelength conversion and optical buffering are viable solutions. The buffer studied here includes both solutions, with full wavelength conversion. It is situated at the output, and handles independent arrivals. We apply an analytic discrete-time queueing model to evaluate performance in terms of loss. We mainly consider the impact of burst size (fixed or varying), scheduling policy, and buffer size. Several numerical examples assess the accuracy of our approximation, and show that our approach is applicable when burst sizes are fixed, and, when a round-robin scheduling policy is adopted, also when burst sizes vary.
We present the analyis of a single-wavelength Fiber-Delay-Line buffer fed by a batch arrival proc... more We present the analyis of a single-wavelength Fiber-Delay-Line buffer fed by a batch arrival process, and apply the results to study the influence of (internal) synchronization on performance. We rely on generating functions to develop a discrete-time queueing model that, unlike previously obtained results, is able to cope with concurrent arrivals. Without making any special assumptions on the burst or batch size distribution, we derive an expression for the scheduling horizon as seen by arriving batches in a system of infinite size. From that, we are able to derive e.g. a maximum tolerable arrival intensity. For finite systems, we use a heuristic to calculate the burst loss probability which is validated against simulations. Consequently, we employ the model assuming a Poisson batch size distribution, and investigate the influence of synchronization. Wether or not this turns out beneficial is shown to relate strongly to the burst size distribution.
Optical burst switching provides a future-proof alternative to the current electronic switching i... more Optical burst switching provides a future-proof alternative to the current electronic switching in the backbone, where buffering is implemented with a set of fiber delay lines (FDLs). Previous performance studies pointed out the related performance loss, but do not allow an exact and general quantification of the impact of correlation. The optical buffer model we constructed considers general inter-arrival times and burst sizes, and is generic and exact for general line lengths. This document provides formulas for waiting time and loss performance. Also, performance graphs illustrate the paramount impact of correlation, that can be determined exactly with the developed model.
Journal of Industrial and Management Optimization, 2010
Abstract: Providing a photonic alternative to the current electronic switching in the backbone, o... more Abstract: Providing a photonic alternative to the current electronic switching in the backbone, optical packet switching (OPS) and optical burst switching (OBS) require optical buffering. Optical buffering exploits delays in long optical fibers; an optical buffer is implemented by routing ...
Abstract—Optical packet switching and burst switching pro-vide future-proof alternatives to the c... more Abstract—Optical packet switching and burst switching pro-vide future-proof alternatives to the current electronic switching in the backbone. To resolve burst (or packet) contention, fiber delay lines are put to use as buffers, as vital part of a channel and delay selection (CDS) ...
In novel switching approaches such as Optical Burst Switching, the involved buffers can only prov... more In novel switching approaches such as Optical Burst Switching, the involved buffers can only provide a degenerate waiting room, with delays restricted to multiples of a basic value, the granularity. Although the resulting performance loss was already studied analytically, previous work is either limited by the assumption of independent arrivals, or it involves a matrix with size growing fast with buffer size or arrival process complexity. Overcoming this, we developed a generic and accurate loss performance model for a degenerate GI/G/1 buffer in discrete time, that yields results instantly for any constellation of burst sizes, inter-arrival times, granularity, load and buffer size. This paper presents our model and compares its results to simulations, illustrating the impact of different types of correlation in the arrival process on loss performance. Our basic model is general and accurate, it can thus serve as a basic tool for optical switch design.
In this paper we present an approach to compute the invariant vector of the N + 1 state Markov ch... more 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.
We investigate the behaviour of an asynchronous single-wavelength fiber delay line (FDL) buffer b... more 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.
ABSTRACT Providing a photonic alternative to the current electronic switching in the backbone, op... more ABSTRACT Providing a photonic alternative to the current electronic switching in the backbone, optical packet switching (OPS) and optical burst switching (OBS) require optical buffering. Optical buffering exploits delays in long optical fibres; an optical buffer is ...
We present a performance model for fiber delay line (FDL) buffers having access to multiple wavel... more We present a performance model for fiber delay line (FDL) buffers having access to multiple wavelengths on an output fiber. In optical burst switching and optical packet switching, contending bursts (or packets) need to be dealt with in an effective way, and both wavelength conversion and optical buffering are viable solutions. The buffer studied here includes both solutions, with full wavelength conversion. It is situated at the output, and handles independent arrivals. We apply an analytic discrete-time queueing model to evaluate performance in terms of loss. We mainly consider the impact of burst size (fixed or varying), scheduling policy, and buffer size. Several numerical examples assess the accuracy of our approximation, and show that our approach is applicable when burst sizes are fixed, and, when a round-robin scheduling policy is adopted, also when burst sizes vary.
We present the analyis of a single-wavelength Fiber-Delay-Line buffer fed by a batch arrival proc... more We present the analyis of a single-wavelength Fiber-Delay-Line buffer fed by a batch arrival process, and apply the results to study the influence of (internal) synchronization on performance. We rely on generating functions to develop a discrete-time queueing model that, unlike previously obtained results, is able to cope with concurrent arrivals. Without making any special assumptions on the burst or batch size distribution, we derive an expression for the scheduling horizon as seen by arriving batches in a system of infinite size. From that, we are able to derive e.g. a maximum tolerable arrival intensity. For finite systems, we use a heuristic to calculate the burst loss probability which is validated against simulations. Consequently, we employ the model assuming a Poisson batch size distribution, and investigate the influence of synchronization. Wether or not this turns out beneficial is shown to relate strongly to the burst size distribution.
Optical burst switching provides a future-proof alternative to the current electronic switching i... more Optical burst switching provides a future-proof alternative to the current electronic switching in the backbone, where buffering is implemented with a set of fiber delay lines (FDLs). Previous performance studies pointed out the related performance loss, but do not allow an exact and general quantification of the impact of correlation. The optical buffer model we constructed considers general inter-arrival times and burst sizes, and is generic and exact for general line lengths. This document provides formulas for waiting time and loss performance. Also, performance graphs illustrate the paramount impact of correlation, that can be determined exactly with the developed model.
Journal of Industrial and Management Optimization, 2010
Abstract: Providing a photonic alternative to the current electronic switching in the backbone, o... more Abstract: Providing a photonic alternative to the current electronic switching in the backbone, optical packet switching (OPS) and optical burst switching (OBS) require optical buffering. Optical buffering exploits delays in long optical fibers; an optical buffer is implemented by routing ...
Abstract—Optical packet switching and burst switching pro-vide future-proof alternatives to the c... more Abstract—Optical packet switching and burst switching pro-vide future-proof alternatives to the current electronic switching in the backbone. To resolve burst (or packet) contention, fiber delay lines are put to use as buffers, as vital part of a channel and delay selection (CDS) ...
In novel switching approaches such as Optical Burst Switching, the involved buffers can only prov... more In novel switching approaches such as Optical Burst Switching, the involved buffers can only provide a degenerate waiting room, with delays restricted to multiples of a basic value, the granularity. Although the resulting performance loss was already studied analytically, previous work is either limited by the assumption of independent arrivals, or it involves a matrix with size growing fast with buffer size or arrival process complexity. Overcoming this, we developed a generic and accurate loss performance model for a degenerate GI/G/1 buffer in discrete time, that yields results instantly for any constellation of burst sizes, inter-arrival times, granularity, load and buffer size. This paper presents our model and compares its results to simulations, illustrating the impact of different types of correlation in the arrival process on loss performance. Our basic model is general and accurate, it can thus serve as a basic tool for optical switch design.
In this paper we present an approach to compute the invariant vector of the N + 1 state Markov ch... more 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.
We investigate the behaviour of an asynchronous single-wavelength fiber delay line (FDL) buffer b... more 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.
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Papers by Wouter Rogiest