This work studies the benefits of heterogeneous cellular networks with overlapping picocells in a large macrocell. We consider three different strategies for resource allocation and cell association. The first model employs a spectrum overlapping strategy with an SINR-based cell association. The second model avoids the interference between macrocell and picocell through a spectrum splitting strategy. Furthermore, picocell range expansion is also considered in this strategy to enable a load balancing between the macrocell and picocells. The last model is a hybrid one, called as fractional spectrum splitting strategy, where spectrum splitting strategy is only applied at the picocell-edge, while the picocell-inner reuses the spectrum of the macrocell. We constructs resource allocation optimization problem for these strategies to maximize the system rate. Our results show that in terms of system rate, all the three strategies outperform the performance of macrocell-only case, which shows the benefit of heterogeneous networks. Moreover, fractional spectrum splitting strategy provides highest system rate at the expense of outage user rate degradation due to inter-macro-pico interference. Spectrum overlapping model provides the second highest system rate gain and also improves outage user rate owing to full spectrum reuse and the benefit of macro diversity, while spectrum splitting model achieves a moderate system rate gain.