Kajamalai G. Ramakrishnan

A case study of multiservice, multipriority traffic engineering design for data networks

We present techniques, some of which are novel, for traffic engineering in QoS-supported data networks, and also illustrate the application of these techniques in a case study. In the interest of scalability all these techniques use multicommodity flow (MCF) solution techniques as primitives. The techniques address the design of topology and size of explicit routes in MPLS-supported IP networks and VPNs. The techniques are for network-wide optimization subject to constraints on routing imposed by end-to-end QoS and other considerations. The notion of admissible route sets specific to service class and source-destination pair is used to differentiate QoS constraints on real-time services, such as Internet telephony and video, and relatively delay insensitive services, such as premium data. Contrasting optimization techniques are given for services, such as best effort, for which no restriction on routes are imposed. Another important traffic engineering requirement addressed is priorities, for which an efficient and accurate design technique is given.

Combined economic modeling and traffic engineering: Joint optimization of pricing and routing in multi-service networks

We consider a network, with fixed topology and link bandwidths, that offers multiple services, such as voice and data, each having characteristic price elasticity to demand, and quality of service and policy requirements on routing. We develop a revenue maximization model in which pricing and routing are jointly optimized. In this model, prices, which depend on service type and origin-destination, determine demands, that are routed, subject to their constraints, so as to maximize revenue, which is earned when the demand is delivered to its destination. The model is flow-based. We study the basic properties of the optimal solution and prove that link shadow costs provide the basis for selecting optimal prices and determining optimal routing policies. We present illustrative numerical examples in which network bandwidth is scaled to grow.

Optimization and design of network routing using refined asymptotic approximations

The problems of route optimization, and the sizing of virtual paths and explicit routes in wide-area multi-service broadband networks are considered. The problems are formulated at the call-level in the framework of multi-rate, circuit-switched, loss networks, with effective bandwidth encapsulating cell and packet-level behavior. Broadband networks are characterized by links with very large capacities in circuits, and are expected to support many services each having a characteristic bandwidth or rate. Various asymptotic results based on Uniform Asymptotic Approximations (UAA) have previously been obtained to reduce the complexity of the numerical calculations. This paper offers refinements (RUAA) to UAA to the loss probabilities for a single link, as well as their sensitivities to the offered traffic. Network loss probabilities are obtained by solving fixed-point equations. Another system of equations determines the implied costs for services and links, which are used to guide the network optimization. Refined asymptotic approximations to the networks loss probabilities as well as to the implied costs are proposed based on the RUAA. The refinements are crucial for the accurate evaluations of the implied costs. The complexity of these calculations remains bounded as the link capacities and traffic intensities become increasingly large, and the complexity for the implied costs is independent of the number of services. A network design tool TALISMAN has been extended to implement the refined approximations. Numerical examples illustrate the accuracy of the RUAA.

Efficient algorithms for location and sizing problems in network design

Large-scale location, sizing and homing problems of distributed network elements, have received much attention recently due to the massive deployment of broadband communication networks for services like Internet telephony and Web caching. Key considerations in designing these networks include modularity of capacity, economies of scale in cost, and reliability. We formulate a general class of such network design problems as Mixed-Integer Programs. These problems are computationally intractable in general; under various asymptotic conditions, we show how to compute near-optimal solutions. To deal with arbitrary instances, we develop new algorithms based on linear programming, as well as greedy randomized adaptive search. These algorithms achieved near-optimal solutions with reasonable computation time for our experiments.

Refined approximations for design and optimization of wide-area, multi-service broadband networks

The problems of route optimization, and the sizing of virtual paths and explicit routes in wide-area multi-service broadband networks are considered. The problems are formulated at the call-level in the framework of multi-rate, circuit-switched, loss networks, with effective bandwidth encapsulating cell and packet-level behavior. Various asymptotic results based on uniform asymptotic approximations (UAA) have previously been obtained to substantially reduce the complexity of the numerical calculations. This paper offers refinements (RUAA) to UAA to the loss probabilities and their sensitivities to the offered traffic for individual links. These results are used to obtain refined asymptotic approximations to the networks loss probabilities and implied costs. While the numerical accuracy is considerably enhanced, the computational complexity remains effectively unchanged. The network design tool TALISMAN has been extended to implement the refined approximations. Numerical examples illustrate the accuracy of the RUAA.