Stationary Waiting Times in m-Node Tandem Queues With Production Blocking

We consider a stationary waiting time in a Poisson driven single-server m-node tandem queue with either constant or non-overlapping service times. Each node except for the first one has a finite buffer, and is operated under production blocking. By using (max,+ )-algebra, we explicitly express the stationary waiting time at each node as a function of finite buffer capacities. We also address that the explicit expression is separable and monotone decreasing with respect to the buffer sizes. These properties are applied to a buffer allocation problem with probabilistic constraints on stationary waiting times.