Reducing Data Center Energy Consumption viaCoordinated Cooling and Load Management

By: Luca Parolini, Bruno Sinopoli, Bruce H. Krogh from CMUPresentation: Liang Hao

Motivation REDUCING the ever growing electricity

consumption in data centers COORDINATING cooling and load

management which is now mostly independent

Previous Work Computational fluid dynamic models to

optimize the delivery of cold air

Optimal load-balancing policy

Temperature-aware manner

Modeling

Modeling(1): Computational network Composed of servers nodes that interact

through the exchange of workloads

This layer interacts with the external world by exchanging jobs

Modeling(2): Thermal network This layer interacts with external world

through electricity consumption Each node in the thermal network has

an input temperature Tin[], an output temperature Tout[] and an electrical power consumption pw[W]

Modeling(3): Server nodes Server node is combined of thermal

server node and computational server node

We assume every server node has a finite number of possible states denoted by the set P. A state p determines the mean execution rate and the power consumption pw, and pw is positively related to

Modeling(4): Server nodes We model the computational server

node as a G/M/1 queue, while the service time is exponentially distributed with parameter (p(t))

the thermal part of server node can be modeled as a first-order linear time-invariant (LTI) system defined by the following differential equation:

Modeling(5): CRAC nodes Tin, Tout, Tref If Tref <= Tin, Tout would tend to Tref Else Tout would tend to Tin pw = f(Tin, Tout)

Modeling(6): Environment nodes pw = 0 Tin, Tout

Modeling(7): Control Inputs Controllable variables: the

computational workload exchange, the server node power states and the CRAC node reference temperature

CMDP Formulation In order to formulate our optimization problem

as a finite CMDP we have to identify: a finite set X of states, a finite set A of actions from which the controller can choose at each step t = k * , a set Pxay of transition probabilities representing the probability of moving from a state x to a state y when the action a is applied, and a function c : X £A ! R of immediate costs for each time step. The total cost over a given time horizon is the sum of the cost incurred at each time step.

CMDP Formulation

CMDP Formulation Server nodes n=3 CRAC node r=1 Environment node e=0 Discrete-time model with time step

CMDP Formulation:Simplification Server1 and server2 do not exchange

tasks Ignore electricity consumption by

server3, the scheduler The overall computational network

workload exchange is reduced to the choice of the mean value of s

CMDP Formulation Quantize Tout and Tref

Solution Use the Markov Decision Process

Toolbox for MATLAB to solve the CMDP problem

Simulation Results

Simulation Results

Simulation Results

What’s insight Build a model that can reflect the real

problem and solve it using mature solutions

To transform a real problem into a mathematical model, we quantize sequential variables into discrete ones