In this paper, we propose a new framework to analyze performance considering finite-length queuing and adaptive modulation and coding for multi-user Voice over IP (VoIP) services in wireless communication systems. We formulate an uplink VoIP system as a two-dimensional discrete-time Markov chain (DTMC) based on a Markov modulated Poisson process traffic model for VoIP services and modulation and coding scheme (MCS)-level set transition reflecting users' channel variations. We extend the transition modeling of the MCS-level for a single-user to the transition modeling of the MCS-level set for multiple users. Since the users can have various MCS combinations in the case of a multi-user system, the MCS-level set transitions are more complicated than the MCS-level transitions of the single-user case. Throughout our DTMC formulation, we present various performance metrics, such as average queue-length, average throughput, packet dropping probability, packet loss probability, and so on. By using the results of the packet loss probability, we can find an optimum packet error rate value that minimizes the total packet loss probability.