Online Algorithms for Routing and Scheduling on Ring Networks

The online packet routing problem is studied in the context of moving data packets efficiently among network nodes. This problem is a special case of the more general k− k routing problem where it is assumed that all packets are known to an algorithm before any packet is sent and each node sends and receives exactly k packets. The online version relaxes these constraints and allows for packets to have arbitary release times and for any number of packets to originate at or to be delivered to any node. The goal of an algorithm is to construct a schedule for any instance with small makespan (maximum completion time) relative to the optimal makespan for a worst case instance. Some algorithms are known for this problem on linear array networks and bidirectional rings. In this paper we investigate better algorithms for rings. First, we provide computer based simulation results in support of an earlier proof that FARTHEST FIRST (FF) scheduling is optimal with respect to makespan on linear arrays. Next we compare different routing algorithms [random routing (RR), probabilistic rotuing (PR), greedy routing (GR), maximum queue length (MQL) and maximum queue length 1 (MQL1)] to shortest path routing (SP) combined with FF scheduling. We then show that none of the above routing algorithms combined with FF is optimal with respect to makespan on bidirectional rings. Lastly, we show that routing affects makespan more than scheduling affects makespan on rings in the average case.