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Published January 1, 1994 | public
Journal Article Open

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 TH,p(r), which can be computed by linear programming, such that for every channel assignment algorithm, T(r) ≤ TH,p(r). Moreover, they show that there exist channel assignment algorithms whose performance approaches TH,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.

Additional Information

© Copyright 1994 IEEE. Reprinted with permission. Manuscript received December 29, 1991; revised December 15, 1992. This work was supported by a grant from GTE Laboratories. The work of R.J. McEliece was supported by the AFOSR under Grant 91-0037 and a grant from Pacific Bell. This paper was presented in part at the 1990 Allerton Conference on Communications, Control, and Computing and at the 3rd IEE Conference on Telecommunications, Edinburgh, Scotland, 1991. A preliminary version of this paper, dealing with uniform traffic on systems described by ordinary graphs, was presented in [13]. The extension to hypergraphs first appeared in [14]. Some other papers on the performance of cellular networks are [3], [7], [8], [10], [17], [18]. Some of the results in [9], whose topic is routing in circuit-switching networks, can also be applied to the analysis of cellular networks, and the relationship between the two problems is further explored in [15]. We thank the referees for their careful reading of the paper, their useful comments, especially on computational complexity, and for the additional references.


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August 22, 2023
August 22, 2023