Suddenly I am in a flow, all the deadlines have passed and nothing is pressuring me anymore. Then there is that emptiness, the sensation that I can choose what to do with my time. I still remember it vaguely from long ago, the time before all the deadlines arrived. Therefore with my spirit up, I start reading papers again. The assignment: find something nice to do with all the mathematics and physics which have accumulated so far. Many interesting papers pass the review and although I see many different things there is one thing that strikes me in particular, the cyber-physical description of a data center has not yet been formally described by my fellow control theorists.

Last time we left off with a way to describe the physics in a data center. Now we continue to study the optimality conditions of the data center through optimal control. Readers eager to understand the details are referred to [1]. For the others, here is a short outline. The problem starts by defining a goal and a way to describe the costs associated to the goal in relevant parameters. For example in a data center the goal is to minimize the power consumption of the equipment and there is a way to calculate the power consumption depending on the total workload, the cooling and the temperature, i.e. the relevant parameters. The second step is to understand the constraints of all your parameters, e.g. a computer has a certain number of processing units, or the temperature has to be kept below a certain threshold. With the tools given to us by optimal control it is now possible to study the optimal point, i.e. the temperature and workload distribution, and the cooling setpoint which results in the minimum power consumption at any given time. The beauty of this all is that we can mathematically study the structure of the optimal point, e.g. what the temperature of the servers will be in the optimal point.

The physical intuition behind the optimal situation is actually rather simple. The servers produce heat by processing jobs and the cooling unit has to do work to remove the heat from the data center. Due to complex airflows the temperature of the servers will vary depending on their location in the data center, however, the cooling unit cannot cool areas individually. Imagine the old air conditioner in the Franckenroom and position yourself in the corner where the television is currently hanging on the wall, on a hot summers day. If you would like to cool that particular spot of the room and turn up the air conditioner to cool that corner, as a consequence you would be cooling the whole room, not only the corner where you are sitting. If there is a hot spot among the servers in the data center and you turn up the cooler to reduce the temperature at that location, as a consequence you are cooling all servers in the data center. Ideally you only want the remove the added heat from the air. This is achieved by dividing the jobs such that the temperature of the servers is equal for all servers. This is not always possible however, but the above mentioned mathematical analysis will tell us when this is the case (namely when servers are maximally loaded). In the next blog I will explain more about how we can use this knowledge to design a controller such that we will always end up in the optimal situation.

[1] Luenberger, D. G. & Ye, Y., Linear and nonlinear programming, Springer, 2016, 4