Multi-token rings and multi-server polling systems: the bang-bang policy

A large variety of distributed communication systems in which SEVERAL stations share one or more channels are modeled as polling systems. Of these applications, the most important one is that of the Token Ring network with either a single token (modeled by a single server polling system) or multiple tokens (modeled by a multiple server polling systera). While much understanding on single token rings (single server polling systems) has been acquired over the years, little is understood about multi-token systems. Most importantly, not much is known about how to efficiently ope rate them. In this work we consider the problem of how to efficiently operate multiple tokens in a ring network. Modeling the system by a polling system, we address the question of how to efficiently operate multiple servers in a multi-queue environment with switch-over times. We demonstrate that the use of a simple cyclic visit order for the servers leads the servers to "stick together" and results in performance degradation since the servers are not evenly spread among the queues; in this system the servers suffer from lack of walk sharing, since they all concurrently waste their time on walking (switching) from queue to queue. An alternative approach in which each of the servers is dedicated to serve a subset of the queues is shown to resolve that problem but suffers from performance degradation due to lack of work sharing by the servers. We discuss the properties of work sharing and walk sharing and demonstrate how the lack of them affects the cyclic server policy and the dedicated server policy. We propose a novel approach, called the \´bang bang\´ policy. with this policy the servers are not dedicated to particular subsets of the queues, and thus the policy allows work sharing among the servers. Furthermore, the policy prevents the servers from \´sticking together" and thus allows for walk sharing among them. As such, the policy overcomes the deficiencies of the other two policies. The ma- n idea of the "bang bang" policy is that afteR the servers meet, they continue to move in opposite directions. Numerical results show that the "bang bang" policy performs significantly better than the other two policies over a wide range of parameters.