  In this paper we consider the problem of maximum throughput for tandem
queueing system. We modeled this system as a Quasi-Birth-Death process. In
order to do this we named level the number of customers waiting in the first
buffer (including the customer in service) and we called phase the state of the
remining servers. Using this model we studied the problem of maximum throughput
of the system: the maximum arrival rate that a given system could support
before becoming saturated, or unstable. We considered different particular
cases of such systems, which were obtained by modifying the capacity of the
intermediary buffers, the arrival rate and the service rates. The results of
the simulations are presented in our paper and can be summed up in the
following conclusions: 1. The analytic formula for the maximum throughput of
the system tends to become rather complicated when the number of servers
increase 2. The maximum throughput of the system converges as the number of
servers increases 3. The homogeneous case reveals an interesting
characteristic: if we reverse the order of the servers, maximum thruoughput of
the system remains unchanged The QBD process used for the case of Poisson
arrivals can be extended to model more general arrival processes.
