Workshop on
Mathematical Modeling and Analysis of Computer Networks
"Two Topics in Networking Research:
InterNetworking and Uncertainty
Management"
Debasis Mitra
Bell Labs, AlcatelLucent
Internetworking 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 dataoptical internetworking,
where routes connecting endpoints 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 internetworking 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 endtoend carried traffic with minimum lightpath provisioning cost, enmeshes data and optical domains. This example of internetworking 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 subproblems, 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 riskadjusted 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 longterm contracts and opportunistic
servicing of random demand, the service provider can optimize its
riskadjusted 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.
