In Section 10.3 we looked at a problem of controlling the arrival rate at an $M/M/1$ queue. Question 3 on Problem Sheet 3 is about controlling the service rate. In both cases, I was using this to illustrate the policy improvement algorithm. In 8.7 I introduced the topic of optimal scheduling in a multi-class $M/G/1$ queue.
Problems about controlling service and/or arrivals, and scheduling, in single queues, or networks of queues, crop up again and again in OR models in communications, supply chains, etc. There is a vast research literature. I have written a few papers about this myself, such as
R. R. Weber and S. Stidham, Jr. Optimal control of service rates in networks of queues. Adv. Appl. Prob. 19, 202-218, 1987.
S. Stidham, Jr and R. R. Weber. Monotonic and insensitive optimal policies for the control of queues with undiscounted costs. Operations Research 37, 611-625, 1989.
S. Stidham and R. Weber. A survey of Markov decision models for control of networks of queues. Queueing Systems 13, 291-314, 1993.
My co-author of those papers, Sandy Stidham, has a huge knowledge of this field. He written a nice article containing 349 references, which gives a bird's eye overview of queueing control and related topics entitled, Applied Probability in Operations Research: A Retrospective, 2001.
If in your own research you ever find that you have reason to want to know more about this subject then I suggest you begin by reading Sandy's retrospective. Or take a look at one of the papers above. The first one is about a problem in which both service and arrival rates can be controlled within a simple network of queues.
Problems about controlling service and/or arrivals, and scheduling, in single queues, or networks of queues, crop up again and again in OR models in communications, supply chains, etc. There is a vast research literature. I have written a few papers about this myself, such as
R. R. Weber and S. Stidham, Jr. Optimal control of service rates in networks of queues. Adv. Appl. Prob. 19, 202-218, 1987.
S. Stidham, Jr and R. R. Weber. Monotonic and insensitive optimal policies for the control of queues with undiscounted costs. Operations Research 37, 611-625, 1989.
S. Stidham and R. Weber. A survey of Markov decision models for control of networks of queues. Queueing Systems 13, 291-314, 1993.
My co-author of those papers, Sandy Stidham, has a huge knowledge of this field. He written a nice article containing 349 references, which gives a bird's eye overview of queueing control and related topics entitled, Applied Probability in Operations Research: A Retrospective, 2001.
If in your own research you ever find that you have reason to want to know more about this subject then I suggest you begin by reading Sandy's retrospective. Or take a look at one of the papers above. The first one is about a problem in which both service and arrival rates can be controlled within a simple network of queues.
