# Survey on Optimization Models for Energy-Efficient Computing Systems

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## Abstract

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## 1. Introduction

#### 1.1. Growth of Energy Consumption by Computing Systems: Reasons and Dynamics

- consumer devices, including personal computers, mobile phones, TVs, and home entertainment systems;
- computer networks;
- data center computation and storage;
- production of ICT equipment.

#### 1.2. Need for Energy Efficiency

#### 1.3. Ways to Reduce Energy Consumption by Computing Systems

## 2. Models That Switch Devices On and Off

#### 2.1. Processor

- reducing the voltage V;
- reducing activity, e.g., by turning off the computer’s unused parts;
- parallel processing, most efficiently by applying it to unrelated tasks.

#### 2.1.1. Efficiency-Oriented Logic

- Clock gating. The idea of this technique is simple and consists of turning the clock tree branches into latches or flip-flops whenever they are not used. Although initially this solution seemed difficult to implement, it is now possible to produce reliable designs with gated clocks.
- Half-frequency and half-swing clocks. The clock frequency can be reduced by 2 at the cost of more complex latches. Lowering the clock swing reduces the energy consumption even more but requires a more sophisticated latch design.
- Asynchronous logic. An advantage of asynchronous logic is that it saves the energy used to power the clock tree. Its drawback is the need to generate completion signals. Thus, additional logic must be used at each register transfer. Asynchronous logic is also difficult to design and test.

#### 2.1.2. Efficiency-Oriented Architecture

- Memory systems. A significant amount of power is used by the memory system. There are two sources of power loss: the frequency of memory access reflected in the second term and the leakage current reflected in the third term of Equation (1).
- Buses. Buses, especially interchip buses, are significant sources of power loss. A chip can expend 15–20% of its power on interchip drivers.
- Parallel processing and pipelining. The conclusion from the analysis of Models (1)–(3) is that parallel processing can significantly reduce power usage in CMOS systems. Pipelining, however, does not possess this advantage. The reason is that it achieves concurrency by increasing the clock frequency and consequently, limits the ability to scale the voltage (see Equation (2)). In practice, however, replicating function units may lead to increasing energy consumption.

#### 2.1.3. Efficiency-Oriented Operation

- dynamic voltage and frequency scaling (DVFS) and dynamic power management (DPM);
- thermal management;
- asymmetric multicore designs.

#### 2.2. Multiprocessor Systems/Data Centers

#### 2.3. Computer Networks

- dedicated and shared protection, where a backup path is assigned to each traffic demand;
- leaving spare capacity on the links along the path.

## 3. Models with Job-Processing Times Depending on Energy Consumption

#### 3.1. Resource-Constrained Scheduling

#### 3.2. Modeling Power as a Continuous Resource

#### 3.3. Modeling Power as a Discrete Resource

## 4. Discussion

#### 4.1. Physical Constraints

#### 4.2. Discretization

## 5. Conclusions

- the quality of the experimental quantum gates;
- the entanglement generated in the QPU.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Yan, Z.; Shi, R.; Yang, Z. ICT Development and Sustainable Energy Consumption: A Perspective of Energy Productivity. Sustainability
**2018**, 10, 2568. [Google Scholar] [CrossRef] [Green Version] - Wang, L.; Zhu, T. Will the Digital Economy Increase Energy Consumption?—An Analysis Based on the ICT Application Research. Chin. J. Urban Environ. Stud.
**2022**, 10, 2250001. [Google Scholar] [CrossRef] - Lange, S.; Santarius, T.; Pohl, J. Digitalization and Energy Consumption. Does ICT Reduce Energy Demand? Ecol. Econ.
**2020**, 176, 106760. [Google Scholar] [CrossRef] - Andrae, A.S. New perspectives on internet electricity use in 2030. Eng. Appl. Sci. Lett.
**2020**, 3, 19–31. [Google Scholar] [CrossRef] - Lorincz, J.; Capone, A.; Wu, J. Greener, Energy-Efficient and Sustainable Networks: State-Of-The-Art and New Trends. Sensors
**2019**, 19, 4864. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Andrae, A.S.G.; Edler, T. On Global Electricity Usage of Communication Technology: Trends to 2030. Challenges
**2015**, 6, 117–157. [Google Scholar] [CrossRef] [Green Version] - Nafus, D.; Schooler, E.M.; Burch, K.A. Carbon-Responsive Computing: Changing the Nexus between Energy and Computing. Energies
**2021**, 14, 6917. [Google Scholar] [CrossRef] - Pruhs, K. Green Computing Algorithmics. In Computing and Software Science: State of the Art and Perspectives; Springer International Publishing: Cham, Switzerland, 2019; pp. 161–183. [Google Scholar] [CrossRef] [Green Version]
- Fagas, G.; Gallagher, J.P.; Gammaitoni, L.; Paul, D.J. Energy Challenges for ICT. In ICT—Energy Concepts for Energy Efficiency and Sustainability; Fagas, G., Gammaitoni, L., Gallagher, J.P., Paul, D.J., Eds.; IntechOpen: Rijeka, Croatia, 2017; Chapter 1. [Google Scholar] [CrossRef] [Green Version]
- Mudge, T. Power: A First-Class Architectural Design Constraint. Computer
**2001**, 34, 52–58. [Google Scholar] [CrossRef] - Lin, M.; Wierman, A.; Andrew, L.L.H.; Thereska, E. Dynamic right-sizing for power-proportional data centers. In Proceedings of the 2011 IEEE INFOCOM, Shanghai, China, 10–15 April 2011; pp. 1098–1106. [Google Scholar] [CrossRef]
- Albers, S.; Moeller, F.; Schmelzer, S. Speed scaling on parallel processors. In Proceedings of the Nineteenth Annual ACM Symposium on Parallel Algorithms and Architectures, San Diego, CA, USA, 9–11 June 2007. [Google Scholar]
- Albers, S. Energy-efficient algorithms. Mag. Commun. ACM
**2010**, 53, 86–96. [Google Scholar] [CrossRef] [Green Version] - Witkowski, M.; Oleksiak, A.; Piontek, T.; Węglarz, J. Practical power consumption estimation for real life HPC applications. Future Gener. Comput. Syst.
**2013**, 29, 208–217. [Google Scholar] [CrossRef] - Barroso, L.; Hölzle, U. The Datacenter as a Computer, An Introduction to the Design of Warehouse-Scale Machines. In Synthesis Lectures on Computer Architecture; Hill, M., Ed.; Morgan Claypol Publishers: Williston, VT, USA, 2009. [Google Scholar]
- Bunde, D. Power-aware Scheduling for Makespan and Flow. In Proceedings of the Eighteenth Annual ACM Symposium on Parallelism in Algorithms and Architectures, Cambridge, MA, USA, 30 July–2 August 2006. [Google Scholar]
- Li, K. Energy Efficient Scheduling of Parallel Tasks on Multiprocessor Computers. J. Supercomput.
**2012**, 60, 223–247. [Google Scholar] [CrossRef] - Bourhnane, S.; Abid, M.; Zine-dine, K.; El Kamoun, N.; Benhaddou, D. High-Performance Computing: A Cost Effective and Energy Efficient Approach. Adv. Sci. Technol. Eng. Syst. J.
**2020**, 5, 1598–1608. [Google Scholar] [CrossRef] - Kormilicin, N.V.; Zhuravlev, A.M.; Khayatov, E.S. Estimation of energy saving in electric drives of traction-blowing mechanisms. In Proceedings of the 2018 17th International Ural Conference on AC Electric Drives (ACED), Ekaterinburg, Russia, 26–30 March 2018; pp. 1–5. [Google Scholar] [CrossRef]
- Gonzalez, R.; Gordon, B.; Horowitz, R. Supply and Threshold Voltage Scaling for Low Power CMOS. IEEE JSSC
**1997**, 32, 1210–1216. [Google Scholar] [CrossRef] [Green Version] - Zhuravlev, S.; Saez, J.C.; Blagodurov, S.; Fedorova, A.; Prieto, M. Survey of Energy-Cognizant Scheduling Techniques. IEEE Trans. Parallel Distrib. Syst.
**2013**, 24, 1447–1464. [Google Scholar] [CrossRef] - Pering, T.; Burd, T.; Brodersen, R. Voltage scheduling in the IpARM Microprocessor system. In Proceedings of the 2000 International Symposium on Low Power Electronics and Design, Rapallo, Italy, 26–27 July 2000. [Google Scholar]
- Burd, T.D.; Brodersen, R.W. Energy Efficient CMOS Microprocessor Design. In Proceedings of the Twenty-Eighth Annual Hawaii International Conference on System Sciences, Wailea, HI, USA, 3–6 January 1995. [Google Scholar]
- Barroso, L.; Hölzle, U. The case for energy- proportional computing. Computer
**2007**, 40, 33–37. [Google Scholar] [CrossRef] - Lin, M.; Wiermn, A.; Andrew, L.; Thereska, E. Dynamic right-sizing for power-proportional data centers. IEEE/ACM Trans. Netw.
**2013**, 21, 1378–1391. [Google Scholar] [CrossRef] - Urgaonkar, R.; Kozat, J.; Igarashi, K.; Neely, M. Dynamic resource allocation and power management in virtualized data centers. In Proceedings of the 2010 IEEE Network Operations and Management Symposium—NOMS 2010, Osaka, Japan, 19–23 April 2010. [Google Scholar]
- Bansal, N.; Gupta, A.; Krishnaswamy, R.; Pruhs, K.; Schewior, K.; Stein, C. A 2-competitive algorithm for online convex optimization with switching costs. In Proceedings of the Workshop on Approximation Algorithms for Combinatorial Optimization Problems, Princeton, NJ, USA, 24–26 August 2015. [Google Scholar]
- Chrobak, M.; Dürr, C.; Hurand, M.; Robert, J. Algorithms for temperature-aware task scheduling in microprocessor systems. In Proceedings of the 4th International Conference on Algorithmic Aspects in Information and Management (AAIM’08), Shanghai, China, 23–25 June 2008. [Google Scholar]
- Bampis, E.; Letsios, D.; Lucarelli, G.; Markakis, E.; Milis, I. On multiprocessor temperature-aware scheduling problems. J. Sched.
**2013**, 16, 529–538. [Google Scholar] [CrossRef] [Green Version] - Birks, M.; Fung, S. Temperature aware online scheduling with a low cooling factor. In Proceedings of the 7th Annual COnference on Theory and Applications of Models of Computation (TAMC’10), Prague, Czech Republic, 7–11 June 2010. [Google Scholar]
- Xiang, Z.; Zheng, Y.; He, M.; Shi, L.; Wang, D.; Deng, S.; Zheng, Z. Energy-effective artificial internet-of-things application deployment in edge-cloud systems. Peer-Netw. Appl.
**2022**, 15, 1029–1044. [Google Scholar] [CrossRef] - Vashisht, P.; Kumar, V. A Cost Effective and Energy Efficient Algorithm for Cloud Computing. Int. J. Math. Eng. Manag. Sci.
**2022**, 7, 681–696. [Google Scholar] [CrossRef] - Yin, G.; Chen, R.; Zhang, Y. Effective task offloading heuristics for minimizing energy consumption in edge computing. In Proceedings of the 2022 IEEE International Conferences on Internet of Things (iThings) and IEEE Green Computing & Communications (GreenCom) and IEEE Cyber, Physical & Social Computing (CPSCom) and IEEE Smart Data (SmartData) and IEEE Congress on Cybermatics (Cybermatics), Espoo, Finland, 22–25 August 2022; pp. 243–249. [Google Scholar] [CrossRef]
- Zhu, Y.; Halpern, M.; Janapa Reddi, V. The Role of the Mobile CPU in Energy-Efficient Mobile Web Browsing. IEEE Micro
**2015**, 35, 26–33. [Google Scholar] [CrossRef] - Corcoran, P.M. Cloud Computing and Consumer Electronics: A Perfect Match or a Hidden Storm? [Soapbox]. IEEE Consum. Electron. Mag.
**2012**, 1, 14–19. [Google Scholar] [CrossRef] [Green Version] - Alcott, B. Jevons’ paradox. Ecol. Econ.
**2005**, 44, 9–21. [Google Scholar] [CrossRef] - Mastelic, T.; Oleksiak, A.; Claussen, H.; Brandic, I.; Pierson, J.M.; Vasilakos, A. Cloud Computing: Survey on Energy Efficiency. ACM Comput. Surv.
**2014**, 47, 1–36. [Google Scholar] [CrossRef] [Green Version] - Addis, B.; Capone, A.; Carello, G.; Gianoli, L.; Sansò, B. Energy management through optimized routing and device powering for greener communication networks. IEEE/ACM Trans. Netw.
**2014**, 22, 313–325. [Google Scholar] [CrossRef] - Addis, B.; Capone, A.; Carello, G.; Gianoli, L.; Sansò, B. On the energy cost of robustness and resiliency in IP networks. Comput. Netw.
**2014**, 75, 239–259. [Google Scholar] [CrossRef] - Błażewicz, J.; Ecker, K.; Pesch, E.; Schmidt, G.; Sterna, M.; Weglarz, J. Handbook on Scheduling; Springer: Berlin/Heidelberg, Germany, 2019. [Google Scholar]
- Leung, J.Y.T. Handbook of Scheduling. Algorithms, Models and Performance Analysis; Chapman&Hall/CRC: Boca Raton, FL, USA, 2004. [Google Scholar]
- Słowiński, R. Two approaches to problems of resource allocation among project activities—A comparative study. J. Oper. Res. Soc.
**1980**, 31, 711–723. [Google Scholar] [CrossRef] - Węglarz, J. On certain models of resources allocation problems. Kybernetes
**1980**, 9, 61–66. [Google Scholar] [CrossRef] - Węglarz, J. Project scheduling with continuously-divisible, doubly constrained resources. Manag. Sci.
**1981**, 27, 1040–1052. [Google Scholar] [CrossRef] - Błażewicz, J.; Cellary, W.; Słowiński, R.; Weglarz, J. Scheduling Under Resource Constraints: Deterministic Models; J.C. Baltzer AG Science Publishers: Basel, Switzerland, 1986. [Google Scholar]
- Węglarz, J. Time-optimal control of resource allocation in a complex of operations framework. IEEE Trans. Syst. Man Cybern.
**1976**, 6, 783–788. [Google Scholar] - Węglarz, J.; Józefowska, J.; Mika, M.; Waligóra, G. Project scheduling with finite or infinite number of activity processing modes—A survey. Eur. J. Oper. Res.
**2011**, 208, 177–205. [Google Scholar] [CrossRef] - Burkov, V. Optimal project control. In Proceedings of the IV IFAC Congress, Warszawa, Poland, 16–21 June 1969. [Google Scholar]
- Węglarz, J. Modelling and control of dynamic resource allocation project scheduling systems. In Optimization and Control of Dynamic Operational Research Models; Tzafestas, S., Ed.; North Holland: Amsterdam, The Netherlands; New York, NY, USA; Oxford, UK; Tokyo, Japan, 1982; pp. 105–140. [Google Scholar]
- Józefowska, J.; Węglarz, J. On a methodology for discrete±continuous scheduling. Eur. J. Oper. Res.
**1998**, 107, 338–353. [Google Scholar] [CrossRef] - Brooks, D.; Bose, P.; Schuster, S.; Jacobson, H.; Kudva, P.; Buyuktosunoglu, A.; Wellman, J.D.; Zyuban, V.; Gupta, M.; Cook, P. Power-aware microarchitecture: Design and modeling challenges for next-generation microprocessors. IEEE Micro
**2000**, 20, 26–44. [Google Scholar] - Józefowska, J.; Mika, M.; Różycki, R.; Waligóra, G.; Węglarz, J. Discrete-continuous scheduling to minimize makespan for power processing rates of jobs. Discret. Appl. Math.
**1999**, 94, 263–285. [Google Scholar] [CrossRef] - Różycki, R.; Węglarz, J. On job models in power management problems. Bull. Pol. Acad. Sci. Tech. Sci.
**2009**, 57, 147–151. [Google Scholar] [CrossRef] [Green Version] - Różycki, R.; Węglarz, J. Power-aware scheduling of preemptable jobs on identical parallel processors to meet deadlines. Eur. J. Oper. Res.
**2012**, 218, 68–75. [Google Scholar] [CrossRef] - Różycki, R.; Węglarz, J. Power-aware scheduling of preemptable jobs on identical parallel processor to minimize makespan. Ann. Oper. Res.
**2014**, 213, 235–252. [Google Scholar] [CrossRef] [Green Version] - Różycki, R.; Waligóra, G. Scheduling identical jobs with linear resource usage profile to minimize schedule length. In Proceedings of the 24th International Conference on Methods and Models in Automation and Robotics, Miedzyzdroje, Poland, 26–29 August 2019. [Google Scholar]
- Yao, F.; Demers, A.; Shenker, S. A scheduling model for reduced cpu energy. In Proceedings of the IEEE Symposium on Foundations of Computer Science, Milwaukee, WI, USA, 23–25 October 1995. [Google Scholar]
- Dror, M.; Stern, H.; Lenstra, J. Parallel machine scheduling with processing rates dependent on number of jobs in operation. Manag. Sci.
**1987**, 33, 1001–1009. [Google Scholar] [CrossRef] - Błażewicz, J.; Lenstra, J.; Rinnooy-Kan, A. Scheduling subject to resource constraints: Classification and complexity. Discret. Appl. Math.
**1983**, 5, 11–24. [Google Scholar] [CrossRef] [Green Version] - Edis, E.B.; Oguz, C.; Ozkarahan, I. Parallel machine scheduling with additional resources: Notation, classification, models and methods. Eur. J. Oper. Res.
**2013**, 230, 449–463. [Google Scholar] [CrossRef] - Daniels, R.L.; Hoopes, B.J.; Mazzola, J.B. Scheduling parellel manufacturing cells with resoure flexibility. Manag. Sci.
**1996**, 42, 1229–1381. [Google Scholar] [CrossRef] - Ruiz-Torres, A.; Centeno, G. Scheduling with flexible resources in parallel workcenters to minimize maximumcompletion time. Comput. Oper. Res.
**2007**, 34, 48–69. [Google Scholar] [CrossRef] - Sue, L.H.; Lien, C.Y. Scheduling parallel machines with resource dependent processing times. Int. J. Prod. Econ.
**2009**, 117, 256–266. [Google Scholar] [CrossRef] - Józefowska, J.; Mika, M.; Różycki, R.; Waligóra, G.; Węglarz, J. Solving the discrete-continuous project scheduling problem via its discretization. Math. Methods Oper. Res.
**2000**, 52, 489–499. [Google Scholar] [CrossRef] - Jaschke, D.; Montangero, S. Is quantum computing green? An estimate for an energy-efficiency quantum advantage. arXiv
**2022**, arXiv:2205.12092. [Google Scholar] [CrossRef] - Aifer, M.; Deffner, S. From quantum speed limits to energy-efficient quantum gates. New J. Phys.
**2022**, 24, 055002. [Google Scholar] [CrossRef]

**Figure 2.**Estimated proportion of energy consumption by ICT sectors in 2030 (Source: based on [7]).

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**MDPI and ACS Style**

Józefowska, J.; Nowak, M.; Różycki, R.; Waligóra, G.
Survey on Optimization Models for Energy-Efficient Computing Systems. *Energies* **2022**, *15*, 8710.
https://doi.org/10.3390/en15228710

**AMA Style**

Józefowska J, Nowak M, Różycki R, Waligóra G.
Survey on Optimization Models for Energy-Efficient Computing Systems. *Energies*. 2022; 15(22):8710.
https://doi.org/10.3390/en15228710

**Chicago/Turabian Style**

Józefowska, Joanna, Mariusz Nowak, Rafał Różycki, and Grzegorz Waligóra.
2022. "Survey on Optimization Models for Energy-Efficient Computing Systems" *Energies* 15, no. 22: 8710.
https://doi.org/10.3390/en15228710