1 Department of Computer Science, University of Cyprus, Nicosia, Cyprus, email: Andreas.Pitsillides@ucy.ac.cy 2 School of Information Technology, Swinburne University of Technology, Melbourne, Australia, 3 Institute of Computer Science, FORTH, Crete, Greece Abstract-We investigate the performance of a classical constrained optimisation (CCO) algorithm and a constrained optimisation Genetic Algorithm (GA) for solving the Bandwidth Allocation for Virtual Paths (BAVP) problem. We compare throughput, fairness and time complexity of GA-BAVP and CCO-BAVP for several node topologies. The results on maximising the throughput obtained with GA-BAVP and CCO- BAVP are in close agreement, however when considering fairness GA-BAVP outperforms CCO-BAVP, especially for more complex topologies, like the 7-node network, without abundant link capacity. Convergence of the two algorithms appears similar, with GA-BAVP outperforming CCO-BAVP in initial stages, and vice-versa for longer time scales. However as the problem complexity increases the solution time for the Genetic Algorithm does not increase as fast as the classical constrained optimisation algorithm. A hybrid scheme is also introduced, combining the benefits of both algorithms. It exhibited better overall convergence rate but the same solution as CCO-BAVP. I. INTRODUCTION High speed integrated services networks (including ATM and recently proposed Internet architectures) aim to support various classes of multimedia traffic with different bit rates and quality of service requirements; thus traffic control and resource management are crucial in order to guarantee the desired grade of service. Several mechanisms are proposed in high speed integrated services networks to allocate resources and control traffic, such as bandwidth allocation, buffer management, call admission control, input rate regulation, routing, and queue scheduling. For Broadband Asynchronous Transfer Mode based networks, it has been suggested that these controls will be applied at different levels such as cell level, burst level, connection (i.e. call) level, Virtual Path (VP) level, and the network level [1]. In order to minimise the complexity of per-call resource management and simplify routing the VP concept was introduced [2], [3]. A VP is a pre-established path between an Origin-Destination (OD) pair. A VP aggregates a number of Virtual Circuits (VCs), and can reserve bandwidth for a time span longer than the duration of a specific call. A primary objective of the VP concept was to facilitate fast and simple call setup with minimum signalling requirements, and allocate call bandwidth at the network edge, by considering only the allocated VP bandwidth. For Internet based networks, current trends are emerging to allocate bandwidth (to different classes and users), in order to support Quality of Service provision (see, for example, [4], [5], [6], [7]). This despite the complexity introduced when compared with the current Internet best-effort model. The architecture of various proposed solutions differ in detail, but the underlying model is similar in the sense that network resources need to be allocated and policed. Aggregated bandwidth allocation, without the need for per-session signalling, is currently advocated for differentiated services (diff-serv) Internet architectures [7]. In this paper we focus on Broadband Asynchronous Transfer Mode based networks, but expect that the findings are also applicable to the Internet models for aggregated bandwidth allocation [7]. Bandwidth Allocation for Virtual Paths (BAVP) aims to supply optimal bandwidth (capacity, service-rate) assignment to VPs by taking global network considerations into account. It is located at the higher levels of the control structure: the VP and network levels. It is therefore associated with a "slow" time scale in terms of minutes or tens of minutes. A number of approaches were proposed to solve the BAVP problem. For example, Gerla et al [8] developed an M/M/1 queuing model (assuming independence between the queues) for BAVP aimed at minimising total expected delays. Hui et al [9] formulated BAVP as a non-linear programming model which minimises total usage cost. Herzberg [10], Herzberg and Pitsillides [11] proposed an alternative model for BAVP which uses a network carrier viewpoint and maximises total network throughput. Ohta and Sato [2] propose a state- dependent, dynamic bandwidth allocation scheme which reallocates bandwidth on a call-by-call basis, i.e. upon arrival of a new call request to a BAVP, and Mocci et al [12] use a periodic approach to reallocate bandwidth to VPs to maximise the network utilisation and achieve a desired call acceptance. The offered traffic in most is characterised by Poisson arrivals, exponential holding time distribution, and constant effective bandwidth. Note that a number of optimisation criteria can be incorporated to formulate a Multiobjective optimisation problem [13] that can also be hierarchically organised [14]. Examples of multiobjective formulations include [15] and [16]. Note that most multiobjective functions are converted to single objective to reduce (considerably) the problem complexity. Also, game theoretic concepts may be used to deal with other issues, such as conflicting objectives, or introducing fairness into the VP BANDWIDTH ALLOCATION FOR VIRTUAL PATHS (BAVP): INVESTIGATION OF PERFORMANCE OF CLASSICAL CONSTRAINED AND GENETIC ALGORITHM BASED OPTIMISATION TECHNIQUES A. Pitsillides 1 , G. Stylianou 1 , C. S. Pattichis 1 , A. Sekercioglu 2 , A. Vasilakos 3