Analysis of an open tandem queueing network with population constraint and constant service times

We consider an open tandem queueing network with population constraint and constant service times. The total number of customers that may be present in the network cannot exceed a given value K. Customers arriving at the queueing network when there are more than K customers are forced to wait in an external queue. The arrival process to the queueing network is assumed to be arbitrary. We show that this queueing network can be transformed into a simple network involving only two nodes. We obtain an upper and lower bound on the mean waiting time. Validations against simulation data establish the tightness of these bounds