File and Work Transfers in Cyclic Queue Systems

A cyclic queue has one server and n nodes, where each node has its own distinct type of customers that arrive from the outside. The server visits the nodes cyclically, serving the customers first at node 1, then at node 2, and so on through node n, and then repeating from node 1 again. Setup times are incurred when the server switches nodes. Typically, in the past, cyclic queues required that the work at any node arrive from the outside only. Our extension permits special nodes termed dual nodes. At these nodes the total work can include not only the outside customers, but also work transferred from other nodes. The transferred work is attended to as a batch at the dual nodes. Dual nodes permit a number of applications to be modeled including computer file transfer, rework in manufacturing, and internal mail delivery. If there are m dual nodes, the expected waiting time calculation requires solution of a linear system of size n(1 + m) + 2m or less. Often the system size is less, and for a queue with one dual node we prove that a system of only size n is required.