Explicit criteria for several types of ergodicity for the length of one kind of M/PH/2 queue

We studied the several types of ergodicity for M/PH/2 queue. For the M/PH/2 queueing system, the queue length L(t) is not a Markov process. But if we supplement a service phase J(t), {L(t),J(t),t = 0} is a Markov process. We also gave a sufficient and necessary condition for l-ergodicity and geometric ergodicity of (L(t),J(t)) for M/PH/2 queue. Moreover, we proved that L(t),J(t),t = 0} is not uniformly ergodic.