Optimal periodical behavior of a multiclass fluid flow network

We consider the optimal scheduling problem of a single server multiclass fluid flow network with non-negligible setup times. The server is able to serve several queues simultaneously, each at its own rate, independent of the number of queues being served. As performance criteria we consider the weighted average amount of fluid in the queues, also known as work in progress, or we consider the cycle time. Restrictions on cycle time and service times are taken into account. A 4-queue server is presented to illustrate the process of deriving the optimal schedule.