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We present an analytical framework for modeling a priority-based load balancing scheme in cellular networks based on a new algorithm called direct retry with truncated offloading channel resource pool (DRK). The model, developed for a baseline case of two cell network, differs in many respects from previous works on load balancing. Foremost, it incorporates the call admission process, through random access. In specific, the proposed model implements the Physical Random Access Channel used in 3GPP network standards. Furthermore, the proposed model allows the differentiation of users based on their priorities. The quantitative results illustrate that, for example, cellular network operators can control the manner in which traffic is offloaded between neighboring cells by simply adjusting the length of the random access phase. Our analysis also allows for the quantitative determination of the blocking probability individual users will experience given a specific length of random access phase. Furthermore, we observe that the improvement in blocking probability per shared channel for load balanced users using (DRK) is maximized at an intermediate number of shared channels, as opposed to the maximum number of these shared resources. This occurs because a balance is achieved between the number of users requesting connections and those that are already admitted to the network. We also present an extension of our analytical model to a multicell network (by means of an approximation) and an application of the proposed load balancing scheme in the context of opportunistic spectrum access.