The following Japanese Temple geometry theorem appears in Fukagawa and Rigby [1]:Thoerem 1: The p... more The following Japanese Temple geometry theorem appears in Fukagawa and Rigby [1]:Thoerem 1: The products of the radii of the excircles on each pair of opposite sides of a circumscribed quadrilateral are equal.See Figure 1. A circumscribed quadrilateral (also called a tangential quadrilateral) is one that possesses an inscribed circle. Now the diagram contains four lines (the sides of the quadrilateral) and one circle S (the inscribed circle) that touches all four of them; this we call the base circle of the theorem. The other four circles each touch just three of the lines. For the moment, assume no two of these lines are parallel, and also assume that no circle apart from S touches all four lines; the exceptional cases will be discussed in Section 4. So any three of the lines are sides of a triangle.
Proceedings of ICC/SUPERCOMM '96 - International Conference on Communications
ABSTRACT Poisson based traffic models do not accurately model the characteristics of many types o... more ABSTRACT Poisson based traffic models do not accurately model the characteristics of many types of real network traffic. Several studies have shown that LAN traffic (and some other types) are well characterized by self-similar processes. Moreover, there are strong indications that traditional Markov queueing systems can overestimate the performance of real ATM systems. We investigate the performance of an ATM queueing system fed by a self-similar arrival process. The packet arrivals are generated by a fractional Brownian noise process and the service process is deterministic. There are no analytical or even numerical solutions for this non-Markov system, therefore we collected our performance measures through simulation. We are able to observe many of the characteristics found in measurement studies. The results are compared to another ATM queueing system with an autoregressive arrival process
Proceedings of ICC '93 - IEEE International Conference on Communications
ABSTRACT Future broadband integrated service digital networks (B-ISDNs) will carry a wide spectru... more ABSTRACT Future broadband integrated service digital networks (B-ISDNs) will carry a wide spectrum of applications with different loss requirements. By adopting a multi-priority scheme at the cell level, flexibility is gained in coping with these diverse requirements in an efficient way. The issue of furnishing a multiclass selective discard mechanism is addressed. The loss probability per class is computed where each class is modeled as a two-state Markov modulated Poisson process (2-MMPP1... 2-MMPPnD/1/K queue). A multiple class buffer priority algorithm that has linear complexity as a function of the number of classes is used. The advantages of a multi-priority scheme as well as the effect of the burstiness on the loss probability are illustrated
A theorem of Van Aubel, which first appeared in concerns the figure obtained by erecting squares ... more A theorem of Van Aubel, which first appeared in concerns the figure obtained by erecting squares on the sides of a quadrilateral, and considering various line segments such as the joins of the centres of opposite squares. In parts of the theorem are extended to the case of (i) four similar rhombi, and (ii) four similar rectangles erected on the sides of a quadrilateral. Further, these two results are described as in some sense ‘dual’ to each other. Here we show that they are in fact both special cases of a further extension of the original theorem (see Proposition 6, and the remarks that follow it), and we also find several extra squares in the original Van Aubel figure (Proposition 11).
IEEE International Conference on Communications, 2003
Reducing packet loss and increasing overall efficiency in multiple source queuing systems is one ... more Reducing packet loss and increasing overall efficiency in multiple source queuing systems is one of the most important issues in the design of traffic control algorithms. On the other hand, the other important issue in such systems is to provide every individual source with the ability to take advantage of a fair portion of the shared available resources such as
In this paper a novel approach for improving packet loss performance in a class of queuing system... more In this paper a novel approach for improving packet loss performance in a class of queuing systems with self-similar characteristics is introduced. The approach takes advantage of a neural-based dynamic buffer management scheme in order to offer an accpetable solution for the existing trade off between the total loss and fairness issues in a typical multiple source system. The significant characteristic of self-similar traffic is the existence of structural similarities across an extremely wide range of time scales. This burst within burst property is one of the unique characteristics of fractal processes. Perceptron neural networks, because of their nonlinear nature, and simple method of learning have shown to be able to provide a powerful tool to model such kind of processes. In this paper, a dynamic neural-based buffer management scheme is used to improve the loss performance of Static Partial Sharing scheme relying on the modeling power of perceptron neural networks. The method ...
The traffic in the future Broadband Integrated Digital Networks will be highly corre- lated and n... more The traffic in the future Broadband Integrated Digital Networks will be highly corre- lated and neglecting its correlations leads to a dramatic underestimation of its perfor- mance. In order to completly specify a queueing network framework, we need to define the stochastic processes resulting from the departure of a queue splitting and merging. In this paper we introduce a procedure for modeling the output process of a multiplexer with Markov modulated input and extend this procedure to model ATM multiplexers with selective discard mechanism. Moreover,we show frameworks for queueing networks with Markov modulated flows which can be used to estimate end-to-end performance in ATM networks.
The following Japanese Temple geometry theorem appears in Fukagawa and Rigby [1]:Thoerem 1: The p... more The following Japanese Temple geometry theorem appears in Fukagawa and Rigby [1]:Thoerem 1: The products of the radii of the excircles on each pair of opposite sides of a circumscribed quadrilateral are equal.See Figure 1. A circumscribed quadrilateral (also called a tangential quadrilateral) is one that possesses an inscribed circle. Now the diagram contains four lines (the sides of the quadrilateral) and one circle S (the inscribed circle) that touches all four of them; this we call the base circle of the theorem. The other four circles each touch just three of the lines. For the moment, assume no two of these lines are parallel, and also assume that no circle apart from S touches all four lines; the exceptional cases will be discussed in Section 4. So any three of the lines are sides of a triangle.
Proceedings of ICC/SUPERCOMM '96 - International Conference on Communications
ABSTRACT Poisson based traffic models do not accurately model the characteristics of many types o... more ABSTRACT Poisson based traffic models do not accurately model the characteristics of many types of real network traffic. Several studies have shown that LAN traffic (and some other types) are well characterized by self-similar processes. Moreover, there are strong indications that traditional Markov queueing systems can overestimate the performance of real ATM systems. We investigate the performance of an ATM queueing system fed by a self-similar arrival process. The packet arrivals are generated by a fractional Brownian noise process and the service process is deterministic. There are no analytical or even numerical solutions for this non-Markov system, therefore we collected our performance measures through simulation. We are able to observe many of the characteristics found in measurement studies. The results are compared to another ATM queueing system with an autoregressive arrival process
Proceedings of ICC '93 - IEEE International Conference on Communications
ABSTRACT Future broadband integrated service digital networks (B-ISDNs) will carry a wide spectru... more ABSTRACT Future broadband integrated service digital networks (B-ISDNs) will carry a wide spectrum of applications with different loss requirements. By adopting a multi-priority scheme at the cell level, flexibility is gained in coping with these diverse requirements in an efficient way. The issue of furnishing a multiclass selective discard mechanism is addressed. The loss probability per class is computed where each class is modeled as a two-state Markov modulated Poisson process (2-MMPP1... 2-MMPPnD/1/K queue). A multiple class buffer priority algorithm that has linear complexity as a function of the number of classes is used. The advantages of a multi-priority scheme as well as the effect of the burstiness on the loss probability are illustrated
A theorem of Van Aubel, which first appeared in concerns the figure obtained by erecting squares ... more A theorem of Van Aubel, which first appeared in concerns the figure obtained by erecting squares on the sides of a quadrilateral, and considering various line segments such as the joins of the centres of opposite squares. In parts of the theorem are extended to the case of (i) four similar rhombi, and (ii) four similar rectangles erected on the sides of a quadrilateral. Further, these two results are described as in some sense ‘dual’ to each other. Here we show that they are in fact both special cases of a further extension of the original theorem (see Proposition 6, and the remarks that follow it), and we also find several extra squares in the original Van Aubel figure (Proposition 11).
IEEE International Conference on Communications, 2003
Reducing packet loss and increasing overall efficiency in multiple source queuing systems is one ... more Reducing packet loss and increasing overall efficiency in multiple source queuing systems is one of the most important issues in the design of traffic control algorithms. On the other hand, the other important issue in such systems is to provide every individual source with the ability to take advantage of a fair portion of the shared available resources such as
In this paper a novel approach for improving packet loss performance in a class of queuing system... more In this paper a novel approach for improving packet loss performance in a class of queuing systems with self-similar characteristics is introduced. The approach takes advantage of a neural-based dynamic buffer management scheme in order to offer an accpetable solution for the existing trade off between the total loss and fairness issues in a typical multiple source system. The significant characteristic of self-similar traffic is the existence of structural similarities across an extremely wide range of time scales. This burst within burst property is one of the unique characteristics of fractal processes. Perceptron neural networks, because of their nonlinear nature, and simple method of learning have shown to be able to provide a powerful tool to model such kind of processes. In this paper, a dynamic neural-based buffer management scheme is used to improve the loss performance of Static Partial Sharing scheme relying on the modeling power of perceptron neural networks. The method ...
The traffic in the future Broadband Integrated Digital Networks will be highly corre- lated and n... more The traffic in the future Broadband Integrated Digital Networks will be highly corre- lated and neglecting its correlations leads to a dramatic underestimation of its perfor- mance. In order to completly specify a queueing network framework, we need to define the stochastic processes resulting from the departure of a queue splitting and merging. In this paper we introduce a procedure for modeling the output process of a multiplexer with Markov modulated input and extend this procedure to model ATM multiplexers with selective discard mechanism. Moreover,we show frameworks for queueing networks with Markov modulated flows which can be used to estimate end-to-end performance in ATM networks.
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