This paper studies a discrete-time, classified multi-server queue with a shared buffer. There are m servers and each server belongs to one of k classes (m≥k), so that k kinds of jobs can be served in the system. The paper characterizes a bursty arrival process using bursts which consist of the same kind of jobs. Once the first job of a burst arrives at the queue, the successive jobs will arrive on every time slot until the last job of the burst arrives. The numbers of jobs of a burst and the inter-arrival times of bursts are assumed to be i.i.d., respectively, and the service time is assumed to be equal to one slot. The paper proposes an efficient numerical method to exactly obtain the job loss probability, the waiting time distribution and the mean queue length. It applies this model to the ATM switch with a shared buffer and obtains the performance measures. Numerical results show the advantage of the ATM switch with a shared buffer compared to the one with output buffers.
