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We consider an admission control problem and adaptive resource allocation for running mobile applications on a cloudlet. We formulate an optimization problem for dynamic resource sharing of mobile users in mobile cloud computing (MCC) hotspot with a cloudlet as a semi-Markov decision process (SMDP). SMDP is transformed into a linear programming (LP) model and it is solved to obtain an optimal solution. In the optimization model, the quality of service (QoS) for different classes of mobile user is taken into account under resource constraints (i.e., bandwidth and server). The numerical results are presented to illustrate that the proposed admission control scheme can achieve a desirable performance and improve throughput of an MCC hotspot significantly.