Workshop on Mathematical Modeling and Analysis of Computer Networks

"Two Topics in Networking Research:
Inter-Networking and Uncertainty Management"

Debasis Mitra
Bell Labs, Alcatel-Lucent

Inter-networking and uncertainty management are among the important challenges of emerging networking. We describe research that touch on both challenges. First, we consider a model of data-optical inter-networking, where routes connecting end-points in data domains are concatenation of segments in the data and optical domains. The optical domain in effect acts as a carrier carrier for multiple data domains. The challenge to inter-networking stems from the limited view that the data and optical domains have of each other. Coordination has to be enabled through parsimonious and qualitatively restrictive information exchange across domains. Yet the overall optimization objective, which is to maximize end-to-end carried traffic with minimum lightpath provisioning cost, enmeshes data and optical domains. This example of inter-networking involves two technologies. A mathematical reflection of the latter fact is the integrality of some of the decision variables due to wavelengths being the bandwidth unit in optical transmission. The problem of optimizing provisioning and routing is decomposed into sub-problems, which are solved by the different domains and the results exchanged in iterations that provably converge to the global optimum.

Next we consider a framework for stochastic traffic management. Traffic demands are uncertain and given by probability distributions. While there are various perspectives (and metrics) to resource usage, such as social welfare and network revenue, we adopt the latter, which is aligned with the service providers interests. Uncertainty introduces the risk of misallocation of resources. What is the right measure of risk in networking? We examine various definitions of risk, some taken from modern portfolio theory, and suggest a balanced solution. Next we consider the optimization of an objective which is a risk-adjusted measure of network revenue. We obtain conditions under which the optimization problem is an instance of convex programming. Studies of the properties of the solution show that it asymptotically meets the stochastic efficiency criterion. We also consider service providers risk mitigation policies. For instance, by selecting the appropriate mix of long-term contracts and opportunistic servicing of random demand, the service provider can optimize its risk-adjusted revenue. The efficient frontier which is the set of Pareto optimal pairs of mean revenue and revenue risk, is useful to the service provider in selecting its operating point.