Random Access in Wireless Networks With Overlapping Cells

We study cellular-like wireless networks in which the cells may overlap substantially, and a common channel is used for all cells. Thus, transmissions intended for one destination (or base station) can cause interference at neighboring destinations. We assume the use of a ¿collision-channel¿ model, in which arbitrary communication and interference regions are associated with each destination. The interaction between such cells is best exemplified if the protocol of access in each cell is pure random access, i.e., Slotted Aloha. We derive a mathematical formula for the maximum achievable throughput for multiple-cell networks that satisfy a ¿balance¿ condition, which is related to (but not as stringent as) symmetry. This formula implies that the throughput achieved in a cell is affected only by the degree of overlap with adjacent cells, i.e., a cell's throughput is not affected by transmissions that are outside of its interference region. Moreover, we show that, at the point of maximum throughput, the expected channel traffic is one packet per slot in each cell, an extension of the result obtained many years ago for single-destination networks.