A finite buffer queue

We consider a queue with finite buffer where the buffer size limits the amount of work that can be stored in the queue. The arrival process is a Poisson or a Markov modulated Poisson process. The service times (packet lengths) are lid with a general distribution. Our queue models the systems in the Internet more realistically than the usual M/GI/1/K queue which restricts the number of packets in the buffer rather than the buffer content (the number of bits). We obtain the stability, the rates of convergence to the stationary distribution and functional limit theorems for this system. In addition we also obtain algorithms to compute the stationary density of the workload process, the waiting times and the probability of packet loss.