Lyapunov stability analysis of load balancing in datacenter networks

Modern datacenters are becoming increasingly complex, with datacenter networks (DCN's) built to meet the data transmission demands of densely interconnected nodes of server hosts and switches. Load balancing in DCN's - to balance the bandwidth utilization among the DCN links - is indispensable for network stability as well as for meeting important objectives such as maximizing throughput and minimizing latency. Simulation has been the de facto empirical method for investigating the stability of DCN's under load balancing policies. To complement simulation with analytical insights into load balancing stability of DCN's, in this paper, we present an application of the qualitative version of the Lyapunov stability theory for load balancing DCN's modeled as discrete-event systems. The general Lyapunov control theory states that a controlled system is stable if there exists a function on the state space of the system, called the Lyapunov function, whose value is non-increasing along any execution trajectory of the system. Analytically proving the existence of such a Lyapunov function is sufficient to verify that the DES model representing a class of DCN's under a load balancing policy is stable. We illustrate the utility of our approach by investigating the stability of a class of DCN's configured in a fat-tree topology under a specific load balancing policy. Our work represents the first step towards a general qualitative stability theory for the policy design of load balancing algorithms for DCN's.