Internet engineering task force (IETF) has proposed hierarchical mobile IPv6 (HMIPv6) in order to reduce a frequent location registration of a mobile node in mobile IPv6 (MIPv6). All traffics toward a mobile node must be transmitted through a MAP in HMIPv6. This brings unnecessary packet latency because of the increased processing cost of packet at the MAP. At this point, the processing cost of packet at the MAP is influenced by the packet arrival rate for a mobile node, cell mobility rate and the number of mobile nodes in MAP domain. In this paper, we analyze the MAP's performance considering the above elements. For this, we compare total cost of HMIPv6 with total cost of MIPv6 as MAP's capability after we define Markov chain model for performance analysis. Also, we define network's total profit as total cost of MIPv6 minus total cost of HMIPv6. Then, we can find optimal capability of MAP such that total profit has maximum value. Also, we use the blocking probability by the MAP's capability as performance estimation element. As a conclusion, we can observe both HMIPv6's performance by the MAP's capability and optimal capability of the MAP, and blocking probability form a relationship of trade off between them.