Conservation laws for dynamic routing in multi-path networks

In this paper, we discuss the feasibility and synthesis aspects of routing algorithms, which have to meet a specified performance criterion. The queuing model for the routing algorithms involves a central router, multiple output queues, each with its own server, deterministic service times, and general, independent, arrival patterns. The performance criterion is the loss probability at each queue, which is specified apriori, and which the router tries to achieve. We analyze this problem using Conservation Laws, and propose a dynamic routing algorithm which tries to achieve the specified criterion. Under certain assumptions, the same theory can be applied to the general class of load balancing problems.