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Channel allocation algorithms for channelized cellular systems are discussed from a new perspective, viz., fairness of allocation. The concepts of relative and absolute fairness are introduced and discussed. It is shown that under certain reasonable assumptions, there exists an absolute (max-min) fair carried traffic intensity vector (a vector describing the traffic carried in the cells of the system). We also show that this vector is unique. We describe some properties of the max-min fair carried traffic intensity vector in an asymptotic limit where the traffic and the number of channels are scaled together. For each traffic pattern, we determine a fixed channel allocation which attains this max-min fair carried traffic intensity vector independent of the value of the offered traffic, in the same asymptotic limit. Finally, we discuss a tradeoff between being max-min fair and trying to maximize revenue. We conclude by discussing some possible extensions of our work.