Network routing control with G-networks

doi:10.1016/j.peva.2010.12.008

Performance Evaluation

Volume 68, Issue 4, April 2011, Pages 320-329

https://doi.org/10.1016/j.peva.2010.12.008 Get rights and content

Abstract

The aim of this paper is to detail a control scheme for packet computer networks whose purpose is to minimise a quality-of-service oriented performance metric by re-routing the traffic. The model is based on G-networks with triggered customer movement to represent traffic re-routing, and on a gradient descent based optimisation algorithm. The model and the algorithm are presented and we show that the gradient descent algorithm is of computational complexity $O (N^{3})$ where $N$ is the number of nodes in the packet network. Via the use of multiple classes of normal traffic and multiple classes of triggers, our approach allows one not only to evaluate the effect of the control, but also to incorporate the overhead that the control traffic will induce, and the consequences of the delays or possible losses of the control traffic. Similarly, these effects will naturally be incorporated when one considers both the impact of the control traffic on the cost function, and the details of this control traffic in the control algorithm itself.

Introduction

G-Networks are queueing networks in which the novel idea of ’negative customers’ has been introduced. In contrast with the regular customers, called positive customers and treated in the normal way by a server, negative customers are also included. “Negative customers” and “signals” can act in the network in several ways: they can destroy a positive customer in a queue [1], trigger the instantaneous passage of a customer to another queue [2] or cause the departure of a batch of customers [3]. This concept of negative customers or signals that can act in the network enhances the queueing network model with control capabilities, thus making G-Networks important and useful in performance modelling.

In the sequel we will present a packet computer network model which is a special case of G-Networks with triggered customer movement [2] including multiple classes [4], [5]. This model offers a theoretical framework to design algorithms that apply control in computer networks by re-routing traffic so as to optimise a given cost function. The model allows one to represent the control traffic itself as a flow of packets which transform themselves into triggers when they reach the target node of the control. Thus, it allows one to analyse not just the effect of the control, but also the overhead and delays that the control packets themselves introduce, and their impact on the details of the control algorithm and on the resulting cost function that one is minimising. In the following sections, we first present an overview of G-Networks and their applications and some background research work on control applied in packet networks in general. Then we present the proposed network model and describe a gradient descent based optimisation algorithm.

Section snippets

G-Networks

G-Networks were initially inspired by neural networks in [6] in which signals can be positive, representing excitatory spikes, or negative, representing inhibitory spikes. A positive spike arriving at a neuron increases its potential by one, while a negative spike arriving at a neuron reduces its potential by one, if its potential is positive, or has no effect if it is zero. When the potential of a neuron is positive, it can send positive or negative signals at random intervals to other neurons

A model of network control

The model we will present is a network model which incorporates the control traffic as well as the control actions taken at each node. It is based on G-Networks [7], [3], [34] and is a special case of G-Networks with triggered customer movement, where the control classes embody the triggers of the mathematical model [2], including multiple classes [4], [5]. In order to provide larger flexibility to the model, we treat links also as ‘nodes’ or ‘queues’. This characteristic enables us to model

Performance metrics

The users’ QoS needs are typically expressed in terms of packet delay, probability of loss, jitter and similar metrics that depend on the congestion at routers and links which in turn depends on the probabilities that the nodes or links are busy. Thus, $q (i, k)$ , $c (l, (i, k))$ and $K (r, (i, k))$ are the key quantities we can use to estimate the QoS metrics.

For example, we can derive the average queue lengths at routers and links. At router $r$ the average queue length for class $k \in U$ , under the assumption of

Gradient descent optimisation

This model allows us to develop a gradient based algorithm for progressive traffic re-routing. As the load values of the network nodes are the important parameters for describing the performance of the network, the routing optimisation can be expressed as the minimization of a generalized cost function $f$ that depends on the $U$ load vectors $q_{k}, \forall k \in U$ $q_{k} = (q_{R} (1, k), q_{R} (2, k), \dots, q_{R} (R, k), q_{L} (1, k), q_{L} (2, k), q_{L} (L, k)) .$ What is also very important, is that the overhead that the control traffic introduces in the

Conclusions

In this paper we have presented a model which describes routing control applied in a packet computer network in order to optimise a performance metric. Specifically, the model is based on G-Networks with triggers which represent the rerouting decisions but in contrast to the usual G-Network model, the control signals are packets which queue up in routers and links, while they transform to signals only at the routers at which they act. Thus, the model incorporates both the conveyance of user

Acknowledgements

The author acknowledges the support for this research from the Fit4Green European Union FP7 Project co-funded under ICT Theme: FP7-ICT-2009-4.

Christina Morfopoulou received her Electrical and Computer Engineering diploma from National Technical University of Athens (NTUA) in 2008, and her M.Sc. degree in Communications and Signal Processing from Imperial College London (ICL) in 2009. Currently she is working towards her Ph.D. in the Intelligent Systems and Networks group of the EEE department of Imperial College London. Her current research interests include energy optimization in networks, network performance and QoS.

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View full text

Network routing control with G-networks

Abstract

Introduction

Section snippets

G-Networks

A model of network control

Performance metrics

Gradient descent optimisation

Conclusions

Acknowledgements

Theoretical Computer Science

European Journal of Operations Research

Performance Evaluation

Product-form queueing networks with negative and positive customers

Journal of Applied Probability

G-networks with instantaneous customer movement

Journal of Applied Probability

G-networks with signals and batch removal

Probability in the Engineering and Informational Sciences

Random neural networks with negative and positive signals and product form solution

Neural Computation

G-networks: an unifying model for queuing networks and neural networks

Annals of Operations Research

The random neural network model for texture generation

International Journal of Pattern Recognition and Artificial Intelligence (IJPRAI)

Minimum cost graph covering with the random network model

Steady-state solution of probabilistic gene regulatory networks

Physical Review B (Condensed Matter)

Network of interacting synthetic molecules in steady state

Proceedings of the Royal Society (Mathematical, Physical and Engineering Sciences)

Random neural networks with synchronised interactions

Neural Computation

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Communications of the ACM

The flow deviation method: An approach to store-and-forward communication network design

Networks