We propose a Lyapunov driftpluspenalty (LDPP) based algorithm to optimize the average power cost for a data center network. In particular, we develop an algorithm to minimize the operational cost using realtime electricity pricing with the integration of green energy resources from the smart grid. The LDPP technique can achieve significant energy cost savings under quality of service (QoS) constraints. Numerical results are presented to evaluate and validate our solution. These results illustrate significant operational/energy cost reductions for a data center network over the conventional approach which optimizes the predicted values of stochastic parameters under a fixed QoS constraint.
Data centers are primary information and communications technology (ICT) energy consumers. For example, data centers in the USA consume 100 billion kWh per year which costs approximately 7.4 billion dollars [
The number of demand applications, particularly video streaming traffic, e.g., video on demand (VoD), web browsing, online gaming, and IPTV, has substantial impact on the energy consumption of data centers and can dynamically change according to the number of user demands. Thus, as emerging services grow as well as the number of connected smart devices rises, the energy consumption of data centers is anticipated to increase significantly.
In the current work, we propose and investigate the performance of a Lyapunov optimization method considering actual realtime prices. Experimental data and computer simulation are used to assess the performance of the LDPPbased energy cost reduction strategy. The results obtained show that this approach can significantly outperform the expected value algorithm (e.g., linear programming or LP (the LP method is a wellknown benchmark method for solving linear constrained optimization problems)) in terms of energy cost savings. In this case, we also derived the probability of violating the QoS (connection delay) and processing (connection handling capacity of the data center) constraints. It is also shown that the proposed LDPP algorithm has a lower probability of violating the QoS and processing constraints compared to the conventional linear programming (LP) approach.
In summary, the main contributions of the present paper are as follows.
We consider energy and cost savings for a data center network in the context of the smart grid. A realtime energy management algorithm is proposed to reduce the cost of server cluster operation according to realtime pricing, energy demand, and power supply estimation. We also incorporate green power generators such as energy storage devices and solar panels as a power supply for the server clusters.
We develop an algorithm based on optimizing the total energy consumption cost in data center networks. This allows us to intelligently route requests among data centers according to the type of user demand application (web/VoD) and energy efficiency considerations.
LP and LDPP methods are investigated to solve the optimization problem. This leads to a tradeoff between operational cost saving and computational complexity.
We examine the number of batteries required to support the average daily streaming traffic for a data center network.
Finally, a probabilistic model is given to model the complementary cumulative distribution function (CCDF) of violating the QoS and processing constraints for data center network users, and the performance with LP and LDPP is compared.
The remainder of this paper is organized as follows. Section
There has been significant research on reducing data center power costs and emissions in the smart grid context [
Previous methods for saving data center power costs can be categorized as minimizing electricity costs [
In [
Different from the approaches in [
Current results in the literature such as in [
In this paper, an optimization model is developed for a data center network based on stochastic parameters extracted from green data centers, and a
The data center model is composed of servers, users, power management control units, the electrical grid, renewable power sources, power storage, and batch schedulers, as illustrated in Figure
Typical data center network including facility and ICT infrastructure with a green power supply including renewable sources (solar panels and wind turbines) and local sources (diesel generators and batteries), as well as sensor controls and internal communications systems.
The power consumption of the computing servers has two major components: static
Electrical energy resources including renewable generators, local power generators (e.g., diesel generators), and batteries for storing energy are illustrated in Figure
Assume that the composite random
The minimization of the power cost can be formulated as an optimization problem with uncertainty
We have considered the composite random
To solve the uncertainty model defined in (
Instead of solving the stochastic constrained optimization model defined in (
Linear programming (LP) can be used as a solution to the expected value in (
In order to employ the Lyapunovdrift algorithm for the above stochastic optimization problem, let
Table
Nomenclature.
Sets and indices  Description 


Number of applications/demands, DCs, and time slot sets 

Index of applications, data centers, 


Parameters  Description 



Positive weighting factors for realtime/elastic applications 

Static power consumption for data center 

Maximum delay for app. 

Number of data centers, time slots 

Mean service time for application 

Positive weighting parameters 

Realtime/elastic probability distribution function 

Penalty function 


Variables  Description 



Number of realtime/elastic connections for application 

Number of realtime/elastic application 

Power amount bought/sold from/to electrical grid at slot 

Power price bought/sold from/to electrical grid at slot 

Amount of renewable generation at slot 

Mean power amount bought/sold from/to electrical grid at slot 

Mean power price bought/sold from/to electrical grid at slot 

Mean renewable generation at slot 

Arrival/departure processes for queue 



Virtual queue 
Let
We now propose a Lyapunov stochastic optimization for the problem formulated in (
The penalty function
Finally, the stochastic optimization model based on the
Observe
Update the queues according to (
Algorithm
Initialize
Set
Set
Greedily choose consumption vector
Convergence checking:
Calculate
As mentioned above, an advantage of the LDPPbased optimization algorithm is that the decision variables depend only on the instantaneous stochastic information without requiring their distribution information. To determine the power cost reduction, we only need to solve a deterministic pertime step problem which validates the effectiveness of the proposed algorithm.
In the proposed constrained optimization problem (
In this section, the probabilities of violating the processing and QoS constraints in (
The probability that the processing constraints are satisfied in the proposed multiapplication/multidata center system, i.e.,
In this section, numerical results are presented to demonstrate the performance of the proposed realtime management algorithm for both the expected value (LP) and Lyapunov optimization solutions. The power cost savings are determined with regards to the optimized amount of grid energy which can be bought and/or sold. To obtain realistic results, we use the actual hourly realtime prices for 24 hour periods from [
It is assumed that the packet generation process follows a Poisson distribution [
The proposed algorithm is evaluated for both LP and LDPP optimization. We compare a regular data center network which only uses the grid for power with a green data center network which uses both the grid and solar panels and balances the power supply and demand using realtime energy management. For simplicity, we only consider realtime traffic for streaming connections. Other types of traffic can be similarly examined.
The number of solar panels is allocated based on the variation in traffic within different data centers. In this case, the number of allocated batteries versus the average daily streaming traffic for a data center network is shown in Figure
Number of batteries for a data center network versus the average number of streaming connections
Figures
Daily cost savings versus the average number of streaming connections
The complementary cumulative distribution function (CCDF) of violating the QoS constraint,
Probability of violating the QoS constraints,
Probability of violating the processing constraints,
Figures
Table
Operational cost and computational complexity comparison of LP and LDPP algorithms for solving energy cost optimization.
SP  Cost reduction ratio %  Execution time reduction ratio %  

LP  LDPP  
500  22  55  2 
800  30  56  9 
1500  41  60  11.5 




SP  LP  LDPP  
500  3.19  3.13  
800  3.48  3.17  
1500  8.09  7.16 
The computation time of the LDPP algorithm and LP approximation for different values of
In this paper, a Lyapunov driftpluspenalty (LDPP) based algorithm was with green energy resources to improve the operational cost of data center networks. The LDPP technique can achieve significant power cost savings via minimizing the longterm average power cost under quality of service (QoS) constraints according to the driftpluspenalty algorithm. Numerical results were presented which demonstrate the reduction in power cost and the robustness of the proposed LDPPbased technique. Moreover, the proposed method has reasonable computational complexity compared to the conventional LP approach. Further, the proposed LDPP method can deliver better quality of service compared to conventional techniques based on the CCDF metric. For future research, machine learning approaches (specifically deep learning) can be used to enhance the system performance in terms of convergence speed and overall cost savings.
The realtime price data used to support the findings of this study are available from [
The authors declare that they have no conflicts of interest.
The authors thank ITRC for its financial support during this research.