Polling systems with routed customers

Summary form only given, as follows. A queuing network that is served by a single server in a cyclic order is studied. Customers arrive at the queues from outside the network according to independent Poisson processes. Upon completion of service, a customer may leave the network, be routed to another queue in the network, or rejoin the same queue for another portion of service. The single server moves along the different queues of the network in a cyclic manner. Whenever the server arrives at a queue (polls the queue), it serves the waiting customers in that queue according to some service discipline. Both the gated and the exhaustive service disciplines are considered. The service time of a customer has a general distribution (which may be different from queue to queue). When moving from one queue to the next queue, the server incurs a switchover period with a general distribution. For this general queuing network the authors derive the expected number of customers present in the network queues at arbitrary epochs and compute the expected delays observed by the customers. In addition, they introduce a pseudoconservation law for this network of queues. Some interesting numerical examples illustrate how routes and server moving direction affect the performance of the network.