Performance bounds for dynamic channel assignment schemes operating under varying re-use constraints

We derive bounds for the performance of dynamic channel assignment (DCA) schemes which strengthen the existing Erlang bound. The construction of the bounds is based on a reward paradigm as an intuitively appealing way of characterizing the achievable carried traffic region. In one-dimensional networks, our bounds closely approach the performance of maximum packing (MP), which is an idealized DCA scheme. This suggests not only that the bounds are extremely tight, but also that no DCA scheme, however sophisticated, can be expected to outperform MP in any significant manner, if at all. Our bounds extend to scenarios with varying re-use which may arise in the case of dynamic re-use partitioning or measurement-based DCA schemes. In these cases, the bounds slightly diverge from the performance of MP, which inflicts higher blocking on outer calls than inner calls, but not to the extent required to maximize carried traffic. This reflects the trade-off that arises in the case of varying re-use between efficiency and fairness. Asymptotic analysis confirms that schemes which minimize blocking intrinsically favor inner calls over outer calls, whereas schemes which do not discriminate among calls inevitably produce higher network-average blocking.