Stretch factor of curveball routing in wireless network: Cost of load balancing

Routing in wireless networks has been heavily studied in the last decade and numerous routing protocols were proposed in literature. Most of the existing routing protocols are based on shortest path routing. Shortest path routing enjoys minimizing the total delay, but may lead uneven distribution of traffic load in a network. For example, wireless nodes in the center of a network usually have heavier traffic load since most of the shortest routes go through the center. To solve this problem, Popa et al. [1] recently proposed a novel routing method, called curveball routing (CBR), which can balance the traffic load and vanish the crowded center effect. In CBR, nodes are mapped on a sphere and packets are routed on those virtual coordinates on the sphere. While CBR achieves better load balancing for the network, it also uses longer routes than the shortest paths. This can be treated as the cost of load balancing. In this paper, we focus on studying this cost of load balancing for curveball routing. Specifically, we theoretically prove that for any network, the distance traveled by the packets using CBR is no more than a small constant factor of the minimum (the distance of the shortest path). The constant factor, we called stretch factor, is only depended on the ratio between the size of the network and the radius of the sphere used in CBR. We then conduct extensive simulations to evaluate the stretch factor and load distribution of CBR and compare them with the shortest path routing in both grid and random networks. We also study the trade-off between stretch factor and load balancing.