We investigate connection-level, packet-level, and energysaving performances in a power constrained (e.g., solar-powered) OFDM/TDMA wireless mesh network. When a mesh router goes to the sleep mode to reduce energy consumption, packet-level performances (as observed by a mesh client) will be degraded since in sleep mode, a mesh router can neither receive nor transmit packets. An analytical model is developed to analyze the relationship among the packet-level and the connection-level performances. Based on the analytical model, the system performance is analyzed in terms of system utility. To this end, an optimization problem is formulated by using a Markov decision process to choose the optimal policy on sleep management and maximum number of admissible connections at a mesh router so that the system utility is maximized.