In this thesis, we study the effects of channel error characteristics on a wireless ATM multiplexing system. The main characteristic of such a channel is that its error behavior is time-varying, with periods of low error rate ( Good ) transmission alternating with periods of high error rates ( Bad ) transmission. This variability is modeled as a two-state Markov chain with two states corresponding to Bad and Good states, respectively. The channel is modeled as being synchronous with the basic time unit being the slot. The transitions from Bad to Good states, and vice versa occur at the slot boundaries. We assume that during a Good state, the channel transmits a packet, while in a Bad state no packet is transmitted. The arrival process is modeled as the superposition of independent binary Markov sources, each source alternates between On and Off periods. In the source Off state, no data is emitted while, in the On state, the source generates a random number of packets in a slot each of which fits into a channel slot. We present a discrete-time queuing analysis of such a system.