Near-optimal spectrum allocation in multi-tier cellular networks with random inelastic traffic

We present a new method for spectrum allocation in a heterogeneous cellular network with multiple tiers of randomly placed base stations and random user session arrivals. Different from previous works, inelastic network traffic is considered, so as to accommodate application sessions with fixed data rate requirements. We first quantify the average downlink sum throughput of the network in terms of a given spectrum allocation vector. We then derive concave upper and lower bounds to the throughput to allow efficient approximate solutions to optimize spectrum allocation. We show that the proposed approach has a worst case optimization performance gap of 12.6% and further demonstrate via simulation that its actual performance is often near optimal.