Cyclic service queues with very short service times

In many applications arising from computer operating systems, telecommunication switching systems, and production processes a resource may be required to handle two or more tasks. Such systems can be analyzed by a cyclic service queueing model consisting of a single server that visits two or more queues according to a hybrid N-policy/T-policy schedule. This schedule is a generalizaton of schedules previously considered by others. Explicit formulae for the average waiting time, the average cycle time and the penalty rate are provided for the case where the service times are sufficiently short relative to the interarrival times that they can be accurately approximated as zero. Optimal schedules are derived for two queue systems and in the multiqueue case for the T-policy. Comparison of schedules is also discussed.