Performance limits for channelized cellular telephone systems

In this paper, we study 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 ceU. For a given channel assignment algorithm, we 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. We show that for a given H and p , there exists a function T H , ~ ( ~ ) , which can be computed by linear programming, such that for every channel assignment algorithm, T(r) 5 T H , ~ ( T ) . Moreover, we show that there exist channel assignment algorithms whose performance approaches TH, p ( r ) arbitrarily closely as the number of channels increases. As a corollary, we show that for a given ( H , p ) there is a number r o , which also can be computed by linear programming, such that if the offered traffic exceeds 7-0, then for any channel assignment algorithm, a positive fraction of all call requests must be blocked, whereas if the offered traffic is less than 1 0 , all call requests can be honored, if the number of channels is sufficiently large. We call r o , whose units are Erlangs per channel, the capacity of the cellular system.