Performance limits for channelized cellular telephone systems
Robert J. McEliece, K.N. Sivarajan · IEEE Transactions on Information Theory · 1994
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/sub H,p/(r), which can be computed by linear programming, such that for every channel assignment algorithm, T(r)/spl les/T/sub H,p/(r). Moreover, they show that there exist channel assignment algorithms whose performance approaches T/sub 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 r/sub 0/, which also can be computed by linear programming, such that if the offered traffic exceeds r/sub 0/, then for any channel assignment algorithm, a positive fraction of all call requests must be blocked, whereas if the offered traffic is less than r/sub 0/, all call requests can be honored, if the number of channels is sufficiently large. The authors call r/sub 0/, whose units are Erlangs per channel, the capacity of the cellular system.>