A queueing analysis of a distributed and energy-aware medium access control (MAC) protocol is presented for wireless ad hoc networks with service differentiation. We consider a battery-powered node in the network with two different types of traffic, and model the node as a MAP/PH/1/K non-preemptive priority queue with multiple vacations to model the sleep and wakeup mechanism of the MAC layer as the server of the queues. Taking into account the non-saturation case for the queueing analysis of the MAC protocol, using phase-type distribution for both the service and the vacation processes, and combining the priority queueing model with the vacation queueing model make the analysis very general and comprehensive.