An integrated multiplexer in intermediate node is analyzed. The multiplexer is modeled as a system with multiple synchronous servers (channels) and having two kinds of customers. Between the two, one is wideband (WB) and the other is narrowband (NB); they are queueable with the same deterministic service time. The WB customer is given higher priority of channel access than the NB. To incorporate the delay constraint of WB, we use a simple instant discarding scheme for WB. As a result, the system states defined just after the beginning of a slot form an one-dimensional embedded Markov chain. This makes the analysis computationally tractable. The performance measures such as queue length distribution, average blocking probability, and average waiting time are obtained, particularly, the waiting time distribution. Some interesting numerical examples are discussed. Simulation results are also provided to help verify the validity of analysis.