Performance limits for channelized cellular telephone systems

Studies the performance of channel assignment algorithms for “channelized” (e.g., FDMA or TDMA) cellular telephone systems, via mathematical models, each of which is characterized by a pair (H,p), where H is a hypergraph describing the channel reuse restrictions, and p is a probability vector describing the variation of traffic intensity from cell to cell. For a given channel assignment algorithm, the authors define T(r) to be the amount of carried traffic, as a function of the offered traffic, where both r and T(r) are measured in Erlangs per channel. They show that for a given H and p, there exists a function T_H,p(r), which can be computed by linear programming, such that for every channel assignment algorithm, T(r)⩽T_H,p(r). Moreover, they show that there exist channel assignment algorithms whose performance approaches T_H,p (r) arbitrarily closely as the number of channels increases. As a corollary, they show that for a given (H,p) there is a number r₀ , which also can be computed by linear programming, such that if the offered traffic exceeds r₀, then for any channel assignment algorithm, a positive fraction of all call requests must be blocked, whereas if the offered traffic is less than r₀, all call requests can be honored, if the number of channels is sufficiently large. The authors call r₀, whose units are Erlangs per channel, the capacity of the cellular system