Comparison of spatial aloha and CSMA using simple stochastic geometry models for 1D and 2D networks

Abstract

Spatial throughput (i.e. throughput with spatial reuse) is important with new types of networks such as vehicular, sensor and military networks. The aim of this study is to compute the spatial throughput of Aloha and CSMA using tools for stochastic geometry. Our network nodes will be modeled as elements of a Poisson Point Process (PPP) of a one- or two-dimensional space. Spatial Aloha can be modeled easily, the transmitting nodes are just selected with a given transmission probability. In spatial CSMA the nodes with the smallest backoff counter in their neighborhood will be selected to transmit and thus we can use random marks to perform the selection. We use the two models we have built to compare the spatial density of successful transmissions of CSMA and Aloha. To carry out a fair comparison, we will optimize both schemes by adjusting their parameters. For spatial Aloha, we can adapt the transmission probability, whereas for spatial CSMA we have to find the suitable carrier sense threshold. The results obtained show that CSMA, when optimized, outperforms Aloha for nearly all the parameters of the network model values and we evaluate the gain of CSMA over Aloha. We also find interesting results concerning the effect of the model parameters on the performance of both Aloha and CSMA. The closed formulas we have obtained provide immediate evaluation of performance, whereas simulations may take minutes to give their results. Even if Aloha and CSMA are old protocols, this comparison of spatial performance is new and provides interesting and useful results.