High-speed packet networks will begin to support services that need Quality-of-Service (QoS) guarantees. Guaranteeing QoS typically translates to reserving resources for the duration of a call. We propose a statedependent routing scheme that builds on any base stateindependent routing scheme, by routing flows which are blocked on their primary paths (as selected by the state-independent scheme) onto alternate paths in a manner that is guaranteed---under certain Poisson assumptions---to improve on the performance of the base state-independent scheme. Our scheme only requires each node to have state information of those links that are incident on it. Such a scheme is of value when either the base state-independent scheme is already in place and a complete overhaul of the routing algorithm is undesirable, or when the state (reserved flows) of a link changes fast enough that the timely update of state information is infeasible to all possible call-originators. The performance improvements ...

Modern communication networks are able to respond to randomly uctuating demands and failures by allowing bu ers to ll, by rerouting tra c and by reallocating resources. They are able to do this so well that, in many respects, largescale networks appear as coherent, almost intelligent, organisms. The design and control of such networks present challenges of a mathematical, engineering and economic nature. In this lecture I describe some of the models that have proved useful in the analysis of stability, statistical sharing and pricing, in systems ranging from the telephone networks of today to the information superhighways of tomorrow.

We compare the performance of a variant of the standard Dynamic Alternative Routing (DAR) technique commonly used in telephone and ATM networks to a path selection algorithm that is based on the balanced allocations principle [4, 18]- the Balanced Dynamic Alternative Routing (BDAR) algorithm. While the standard technique checks alternative routes sequentially until available bandwidth is found, the BDAR algorithm compares and chooses the best among a small number of alternatives. We show that, at the expense of a minor increase in routing overhead, the BDAR gives a substantial improvement in network performance in terms of both network congestion and blocking probabilities. 1

This paper examines the connection between loss networks without controls and Markov random field theory. The approach taken yields insight into the structure and computation of network equilibrium distributions, and into the nature of spatial dependence in networks. In addition, it provides further insight into some commonly used approximations, enables the development of more refined approximations, and permits the derivation of some asymptotically exact results. 1

Emerging high speed Broadband Integrated Services Digital Networks (B-ISDN) are expected to carry traffic for services like video-on-demand and video teleconferencing which will require resource reservation along the path on which the traffic is sent. As a result, such networks will need efficient routing and admission control algorithms. The simplest approach is to use fixed paths and no admission control. More sophisticated approaches which use state dependent routing and a form of admission control called trunk reservation can be found in the circuit switching literature. However, the circuit switching literature has generally focused on fully connected (complete) networks. This paper suggests a new routing and admission control algorithm for general topology networks. Our algorithm is an adaptation of a recently discovered theoretical algorithm that is asymptotically best possible with respect to the worst case performance. The main idea behind our algorithm was to improve the per...

: This paper is concerned with the performance evaluation of loss networks. For the simplest networks there are explicit analytical formulae for the important measures of performance, but for networks which involve some level of dynamic control, exact analytical methods have had only limited success. Under several regimes the Erlang Fixed Point (EFP) method provides a good approximation for the blocking probabilities, but when these regimes are not operative the method can perform badly. In many cases this is because the key assumption of independent blocking does not hold. We derive methods for estimating the blocking probabilities which specifically account for the dependencies between neighbouring links. For the network considered here, namely a ring network with two types of traffic, our method produced relative errors typically 10 \Gamma5 of that found using the EFP approximation. 1. INTRODUCTION We shall be concerned with circuit-switched networks of the kind depicted in Figu...

. This paper reviews some current work on routing in loss and queueing networks. We describe two classes of bound on the performance of any dynamic routing scheme, together with some open questions concerning whether the bounds can be approached under certain limiting regimes. The first class of bound is particularly appropriate for networks in heavy traffic, where the key feature of a good routing scheme is its effective utilization of various pooled resources identified by a fluid version of the routing problem. The second class of bound is particularly appropriate for highly connected networks, with many alternative paths. Again, a network flow representation is central, but this time involving a collection of Markov decision processes, one for each resource of the network. Despite their simplicity, the bounds are able to identify the great variety of qualitatively distinct behaviour expected of a good dynamic routing scheme, depending on a network's size, connectivity, asymmetry an...

We compare the long-term, steady-state performance of a variant of the standard Dynamic Alternative Routing (DAR) technique commonly used in telephone and ATM networks, to the performance of a path-selection algorithm based on the “balanced-allocation ” principle [3, 17]; we refer to this new algorithm as the Balanced Dynamic Alternative Routing (BDAR) algorithm. While DAR checks alternative routes sequentially until available bandwidth is found, the BDAR algorithm compares and chooses the best among a small number of alternatives. We show that, at the expense of a minor increase in routing overhead, the BDAR algorithm gives a substantial improvement in network performance, in terms both of network congestion and of bandwidth requirement.

We introduce penalty function based admission control policies to approximately maximize the expected reward rate in a loss network. These control policies are easy to implement and perform well both in the transient period as well as in steady state. A major advantage of the penalty approach is that it avoids solving the associated dynamic program. However, a disadvantage of this approach is that it requires the capacity requested by individual requests to be su#ciently small compared to total available capacity. We first solve a related deterministic linear program (LP) and then translate an optimal solution of the LP into an admission control policy for the loss network via an exponential penalty function. We show that the penalty policy is a target-tracking policy -- it performs well because the optimal solution of the LP is a good target ! We demonstrate that the penalty approach can be extended to track arbitrarily defined target sets. Results from preliminary simulation studies are included.

The thesis concentrates on design, analysis, and implementation of efficient algorithms for large scale optimization problems with special emphasis on problems related to network flows and routing in high-speed networks. The main focus is on using continuous techniques for solving large combinatorial optimization problems in off-line and online settings. Some of the major areas of work include: ffl Developing and implementing new interior-point techniques for efficiently solving large scale multi-commodity network flow problems. These algorithms are based on solving linear and quadratic programming formulations of the problem. ffl Designing fast algorithms based on continuous methods for approximate solution of minimum cost multi-commodity flow problem. These techniques are geared towards distributed implementation. ffl Application of multi-commodity flow techniques for design and implementation of centralized and distributed algorithms for on-line routing of Virtual Circuits in AT...