We study the problem of inter cell interference coordination (ICIC) with fixed transmit power in OFDMA-based cellular networks, in which each base station (BS) needs to decide as to which subchannel, if any, to allocate to each of its associated mobile stations (MS) for data transmission. In general, there exists a trade-off between the total throughput (sum of throughputs of all the MSs) and fairness under the allocations found by resource allocation schemes. We introduce the concept of $τ-α-$fairness by modifying the concept of $α-$fairness, which was earlier proposed in the context of designing fair end-to-end window-based congestion control protocols for packet-switched networks. The concept of $τ-α-$fairness allows us to achieve arbitrary trade-offs between the total throughput and degree of fairness by selecting an appropriate value of $α$ in $[0,\infty)$. We show that for every $α\in [0,\infty)$ and every $τ> 0$, the problem of finding a $τ-α-$fair allocation is NP-Complete. Further, we show that for every $α\in [0, \infty)$, there exist thresholds such that if the potential interference levels experienced by each MS on every subchannel are above the threshold values, then the problem can be optimally solved in polynomial time by reducing it to the bipartite graph matching problem. Also, we propose a simple, distributed subchannel allocation algorithm for the ICIC problem, which is flexible, requires a small amount of time to operate, and requires information exchange among only neighboring BSs. We investigate via simulations as to how the algorithm parameters should be selected so as to achieve any desired trade-off between the total throughput and fairness.