Skip to main content

Advertisement

Log in

Energy-efficient adaptive networked datacenters for the QoS support of real-time applications

  • Published:
The Journal of Supercomputing Aims and scope Submit manuscript

Abstract

In this paper, we develop the optimal minimum-energy scheduler for the adaptive joint allocation of the task sizes, computing rates, communication rates and communication powers in virtualized networked data centers (VNetDCs) that operate under hard per-job delay-constraints. The considered VNetDC platform works at the Middleware layer of the underlying protocol stack. It aims at supporting real-time stream service (such as, for example, the emerging big data stream computing (BDSC) services) by adopting the software-as-a-service (SaaS) computing model. Our objective is the minimization of the overall computing-plus-communication energy consumption. The main new contributions of the paper are the following ones: (i) the computing-plus-communication resources are jointly allotted in an adaptive fashion by accounting in real-time for both the (possibly, unpredictable) time fluctuations of the offered workload and the reconfiguration costs of the considered VNetDC platform; (ii) hard per-job delay-constraints on the overall allowed computing-plus-communication latencies are enforced; and, (iii) to deal with the inherently nonconvex nature of the resulting resource optimization problem, a novel solving approach is developed, that leads to the lossless decomposition of the afforded problem into the cascade of two simpler sub-problems. The sensitivity of the energy consumption of the proposed scheduler on the allowed processing latency, as well as the peak-to-mean ratio (PMR) and the correlation coefficient (i.e., the smoothness) of the offered workload is numerically tested under both synthetically generated and real-world workload traces. Finally, as an index of the attained energy efficiency, we compare the energy consumption of the proposed scheduler with the corresponding ones of some benchmark static, hybrid and sequential schedulers and numerically evaluate the resulting percent energy gaps.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Notes

  1. In the sequel, we understand the dependence on the slot index \(m\) when it is not strictly demanded.

  2. Since \(L_\mathrm{tot}\) is expressed in (bits), we express \(f_{c}\) in (bit/s). However, all the presented developments and formal properties still hold verbatim when \(L_\mathrm{tot}\) is measured in \(Jobs\) and, then, \(f_{c}\) is measured in (Jobs/cycle). Depending on the considered application scenario, a job may be a bit, frame, datagram, segment, or an overall file record.

  3. Formally speaking, the primal–dual algorithm is an iterative procedure for solving convex optimization problems, which applies quasi-Newton methods for updating the primal–dual variables [52, pp.407-408]. See the Appendix A for the analytic details.

  4. Proposition 4 proves that, for any assigned \(\mu ^{(n)}\), the relationship in (26c) gives the corresponding optimal \(L_i^{(n)}\), \(i=1,\ldots ,M\). This implies, in turn, that \(U^{(n-1)}(.)\) in (B.1) vanishes if and only if the global optimum is attained, that is, at \(L_i^{(n-1)}= L_i^*\), for any \(i=1,\ldots ,M\).

  5. About this point, the formal assumption of Sect. 2 guarantees that: (i) \(\pi _i^{-1}(.)\) in (26b) is strictly increasing in \(\nu _i^{(n)}\) over the feasible set \(\left[ f_i^{\min },f_i^{\max }\right] \); (ii) \(\left( \partial P_i^{net}(R_i)/\partial R_i\right) ^{-1}(.)\) in (26c) is strictly increasing in \(\mu ^{(n)}\); and, (iii) \(\nu _i^{(n)}\) in (26a) is strictly increasing in \(\mu ^{(n)}\) for \(\nu _i^{(n)}>0\). Hence, the condition: \(\mu ^{(n)}<\mu ^{(n-1)}\) guarantees that: \(L_i^{(n)}<L_i^{(n-1)}\), for any \(i=1,\ldots ,M\).

References

  1. Cugola G, Magara A (2012) Processing flows of information: from data stream to complex event processing. ACM Comput Surveys (CSUR) 44(3)

  2. Baliga J, Ayre RWA, Hinton K, Tucker RS (2011) Green cloud computing: balancing energy in processing. Storage Transp Proc IEEE 99(1):149–167

    Google Scholar 

  3. Mishra A, Jain R, Durresi A (2012) Cloud computing: networking and communication challenges. IEEE Commun Mag 50(9):24–25

  4. Azodolmolky S, Wieder P, Yahyapour R (2013) Cloud computing networking: challanges and opportunities for innovations. IEEE Commun Mag 51(7):54–62

  5. Scheneider S, Hirzel M, Gedik B (2013) Tutorial: stream processing optimizations. ACM DEBS 249–258

  6. Lu T, Chen M (2012) Simple and effective dynamic provisioning for power-proportional data centers. Proc CISS

  7. Rajaraman A, Ullman JD (2011) Mining of massive datasets. Cambridge University Press, Cambridge, p 326

  8. Chakravarthy Sh, Jiang Q (2009) Stream data processing: a quality of service perspective, vol 36. Springer, Berlin, p 348

  9. Krempl G, Brzezinski D, Hllermeier E, Last M (2014) Open challenges for data stream mining research. ACM SIGKDD Explor Newslett

  10. Mittal S (2014 ) Power management techniques for data centers: a survey. arXiv:1404.6681

  11. Baccarelli E, Biagi M, Pelizzoni C, Cordeschi N (2007) Optimized power allocation for multiantenna systems impaired by multiple access interference and imperfect channel estimation. IEEE Trans Veh Technol 56(5):3089–3105

    Article  MathSciNet  Google Scholar 

  12. Neumeyer L, Robbins B, Nair A, Kesari A (2010) S4: distributed stream computing platform. In: International workshop on knowledge discovery using cloud and distributed computing platforms, ICDMW ’10, pp 170–177

  13. Zaharia M, Das T, Li H, Shenker S, Stoica I (2012) Discretized streams: an efficient and fault-tolerant model for stream processing on large clusters. Hot Cloud

  14. Loesing S, Hentschel M, Kraska T (2012) Storm: an elastic and highly available streaming service in the cloud. EDBT-ICDT ’12, pp 55–60

  15. Qian Z, He Y, Su C, Wu Z, Zhu H, Zhang T (2013) TimeStream: reliable stream computation in the cloud. In: EuroSys, pp 1–14

  16. Kumbhare A et al (2014) PLAstiCC: predictive look-ahead scheduling for continuous data- flows on clouds. CCGRID

  17. Mathew V, Sitaraman R, Rowstrom A (2012) Energy-aware load balancing in content delivery networks. IEEE INFOCOM

  18. Padala P, You KY, Shin KG, Zhu X, Uysal M, Wang Z, Singhal S, Merchant M (2009) Automatic control of multiple virtualized resources. . In: Proceedings of the 4th ACM European conference on computer systems, pp 13–26

  19. Kusic D, Kandasamy N (2008) Power and performance management of virtualized computing environments via look-ahead control. . In: Proceedings of the international conference on automatic computing, vol 1, pp 3–12

  20. Govindan S, Choi J, Urgaonkar B, Sasubramanian A, Baldini A (2009) Statistical profiling-based techniques for effective power provisioning in data centers. Proc Euro Syst

  21. Lin M, Wierman A, Andrew L, Thereska E (2011) Dynamic right-sizing for power-proportional data centers. IEEE INFOCOM

  22. Zhou Z et al (2013) Carbon-aware load balancing for geo-distributed cloud services. IEEE MASCOTS, pp 232–241

  23. Tamm O, Hersmeyer C, Rush AM (2010) Eco-sustainable system and network architectures for future transport networks. Bell Labs Tech J 14:311–327

    Article  Google Scholar 

  24. Liu J, Zhao F, Liu X, He W (2009) Challenges towards elastic power management in internet data centers. In: Proceedings on IEEE international conference on distributed computing systems workshops, Los Alamitos

  25. Khan AN, Mat Kiah ML, Madani SA, Ali M, Khan AR, Shamshirband S (2014) Incremental proxy re-encryption scheme for mobile cloud computing environment. J Supercomput 68(2):624–651

  26. Nathuji R, Schwan K (2007) VirtualPower: coordinated power management in virtualized enterprise systems. In: ACM 21th SOSP’07, pp 265–278

  27. Kim KH, Beloglazov A, Buyya R (2009) Power-aware provisioning of cloud resources for real-time services. Proc ACM MGC’09

  28. Koller R, Verma A, Neogi A (2010) WattApp: an application aware power meter for shared data centers. ICAC’10

  29. Warneke D, Kao O (2011) Exploiting dynamic resource allocation for efficient parallel data processing in the cloud. IEEE Trans Parallel Disturb Syst 22(6):985–997

    Article  Google Scholar 

  30. Zhu D, Melhem R, Childers BR (2003) Scheduling with dynamic voltage/rate adjustment using slack reclamation in multiprocessor real-time systems. IEEE Trans Parllel Distrib Syst 14(7):686–700

    Article  Google Scholar 

  31. Vasudevan V et al (2009) Safe and effective fine-grained TCP retransmissions for datacenter communication. ACM SIGCOMM, pp 303–314

  32. Alizadeh M, Greenberg A, Maltz DA (2010) J Padhye “Data center TCP (DCTCP)”, ACM SIGCOMM.

  33. Das T, Sivalingam KM (2013) TCP improvements for data center networks. COMSNETS, pp 1–10

  34. Kurose JF, Ross KW (2013) Computer networking: a top-down approach featuring the internet, 6th edn. Addison Wesley

  35. Jin S, Guo L, Matta I, Bestravos A (2003) A spectrum of TCP-friendly window-based congestion control algorithms. IEEE/ACM Trans Netw 11(3):341–355

    Article  Google Scholar 

  36. Baccarelli E, Biagi M, Pelizzoni C, Cordeschi N (2008) Optimal MIMO UWB-IR transceiver for Nakagami-fading and Poisson-arrivals. J Commun 3(1):27–40

    Article  Google Scholar 

  37. Cordeschi N, Patriarca T, Baccarelli E (2012) Stochastic traffic engineering for real-time applications over wireless networks. J Netw Comput Appl 35(2):681–694

    Article  Google Scholar 

  38. Baccarelli E, Cordeschi N, Polli V (2013) Optimal self-adaptive QoS resource management in interference-affected multicast wireless networks. IEEE/ACM Trans Netw 21(6):1750–1759

    Article  Google Scholar 

  39. Al-Fares M, Loukissas A, Vahdat A (2008) A scalable commodity data center network architecture. ACM SIGCOMM, pp 63–74

  40. Gulati A, Merchant A, Varman PJ (2010) mClock: handling throughput variability for hypervisor IO scheduling, OSDI’10

  41. Ballami H, Costa P, Karagiannis T, Rowstron A (2011) Towards predicable datacenter networks, SIGCOMM ’11

  42. Greenberg A et al (2011) VL2: a scalable and flexible data center network. Commun ACM 54(3):95–104

  43. Guo C et al (2010) SecondNet: a data center network virtualization architecture with bandwidth guarantees. ACM CoNEXT

  44. Xia L, Cui Z, Lange J (2012) VNET/P: bridging the cloud and high performance computing through fast overaly networking, HPDC’12

  45. Wang L, Zhang F, Aroca JA, Vasilakos AV, Zheng K, Hou C, Li D, Liu Z (2014) Green DCN: a general framework for achieving energy efficiency in data center networks. IEEE JSAC 32(1):4–15

    Google Scholar 

  46. Khan AN, Mat Kiah ML, Ali M, Madani SA, Khan AR, Shamshirband S (2014) BSS: block-based sharing scheme for secure data storage services in mobile cloud environment. J Supercomput. doi:10.1007/s11227-014-1269-8

  47. Neely MJ, Modiano E, Rohs CE (2003) Power allocation and routing in multi beam satellites with time-varying channels. IEEE/ACM Trans Netw 19(1):138–152

    Article  Google Scholar 

  48. Wang L, Zhang F, Hou C, Aroca JA, Liu Z (2013) Incorporating rate adaptation into Green networking for future data centers. IEEE NCA, pp 106–109

  49. Balter MH (2013) Performance modeling and design of computer systems. Cambridge Press, Cambridge

  50. Chiang M, Low SH, Calderbank AR, Doyle JC (2007) Layering as optimization decomposition: a mathematical theory of network architectures. Proc IEEE 95(1):255–312

    Article  Google Scholar 

  51. Cordeschi N, Shojafar M, Baccarelli E (2013) Energy-saving self-configuring networked data centers. Comput Netw 57(17):3479–3491

    Article  Google Scholar 

  52. Bazaraa MS, Sherali HD, Shetty CM (2006) Nonlinear programming, 3rd edn. Wiley, New York

  53. Kushner HJ, Yang J (1995) Analysis of adaptive step-size SA algorithms for parameter tracking. IEEE Trans Autom Control 40(8):1403–1410

    Article  MATH  MathSciNet  Google Scholar 

  54. Baccarelli E, Cusani R (1996) Recursive Kalman-type optimal estimation and detection of hidden Markov chains. Signal Process 51(1):55–64

    Article  MATH  Google Scholar 

  55. Urgaonkar B, Pacifici G, Shenoy P, Spreitzer M, Tantawi A (2007) Analytic modeling of multitier internet applications. ACM Trans Web 1(1)

  56. Srikant R (2004) The mathematics of internet congestion control. Birkhauser, Basel

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Enzo Baccarelli.

Appendices

Appendix A: Derivations of Eqs. (21a)–(23)

Since the constraint in (10g) is already accounted for by the feasibility condition (18b), without loss of optimality, we may directly focus on the resolution of optimization problem in (16) under the constraints in (10b)–(10e). Since this problem is strictly convex and all its constraints are linear, the Slater’s qualification conditions hold [52, chap.5], so that the Karush–Khun–Tucker (KKT) conditions [52, chap.4] are both necessary and sufficient for analytically characterizing the corresponding unique optimal global solution. Before applying these conditions, we observe that each power-rate function in (17) is increasing for \(L_i\ge 0\), so that, without loss of optimality, we may replace the equality constraint in (10c) by the following equivalent one: \(\sum _{i=1}^M L_i\ge L_\mathrm{tot}\). In doing so, the Lagrangian function of the afforded problem reads as in

$$\begin{aligned}&\mathcal {L}\left( \left\{ L_i,f_i,\nu _i,\mu \right\} \right) \equiv \mathcal {Z}\left( \left\{ L_i,f_i\right\} \right) \sum _{i=1}^M \nu _i\left( L_i-f_i\Delta +L_b(i)\right) +\mu \left( L_t-\sum _{i=1}^ML_i\right) , \end{aligned}$$
(A.1)

where \(\mathcal {Z}\left( \left\{ L_i,f_i\right\} \right) \) indicates the objective function in (16), \(\nu _i\)’s and \(\mu \) are nonnegative Lagrange multipliers and the box constraints in (10d), (10e) are managed as implicit ones. The partial derivatives of \(\mathcal {L}(.;.)\) with respect to \(f_i\), \(L_i\) are given by

$$\begin{aligned} \frac{\partial \mathcal {L}(.)}{\partial f_i}=\frac{\mathcal {E}_i^\mathrm{max}}{f_i^\mathrm{max}} \frac{\partial \Phi _i(f_i/f_i^\mathrm{max})}{\partial \eta _i}+2k_e\left( f_i-f_i^0\right) -\nu _i\Delta , \end{aligned}$$
(A.2)
$$\begin{aligned} \frac{\partial \mathcal {L}(.)}{\partial L_i}= 2 \frac{\partial }{\partial R_i}P_i^\mathrm{net} \left( \frac{2L_i}{T_t-\Delta }\right) +\nu _i-\mu , \end{aligned}$$
(A.3)

\(i=1,\ldots ,M\), while the complementary conditions [52, chap.4] associated to the constraints present in (A.1) read as in

$$\begin{aligned} \nu _i\left[ L_i-f_i\Delta +L_b(i)\right] =0,\quad i = 1,\ldots ,M;\;\; \mu \left( L_\mathrm{tot}-\sum _{i=1}^M L_i\right) =0. \end{aligned}$$
(A.4)

Hence, by equating (A.2) to zero we directly arrive at (21a), that also accounts for the box constraint: \(f_i^{\min }\le f_i\le f_i^{\max }\) through the corresponding projector operator. Moreover, a direct exploitation of the last complementary condition in (A.4) allows us to compute the optimal \(\mu ^*\) by solving the algebraic equation in (23). To obtain the analytical expressions for \(L_i^*\) and \(\nu _i^*\), we proceed to consider the two cases of \(\nu _i^*>0\) and \(\nu _i^*=0\). Specifically, when \(\nu _i^*\) is positive, the \(i\)th constraint in (10b) is bound [see (A.4)], so that we have

$$\begin{aligned} L_i^*=\Delta f_i^*-L_b(i),\;\; \text{ at } \nu _i^*>0. \end{aligned}$$
(A.5)

Hence, after equating (A.3) to zero, we obtain the following expression for the corresponding optimal \(\nu _i^*\):

$$\begin{aligned} \nu _i^*=\mu ^*-2\left[ \frac{\partial P_i^\mathrm{net}}{\partial R_i}\left( \frac{2L_i^*}{T_t-\Delta }\right) \right] , \quad \text{ at } \nu _i^*>0. \end{aligned}$$
(A.6)

Since \(L_i^*\) must fall into the closed interval \([0,\Delta f_i^*-L_b(i)]\) for feasible CPOPs [see (10b), (10e)], at \(\nu _i^*=0\), we must have: \(L_i^*=0\) or \(0<L_i^*<\Delta f_i^*-L_b(i)\). Specifically, we observe that, by definition, vanishing \(L_i^*\) is optimal when \(\left[ \partial \mathcal {L}/\partial L_i\right] _{L_i=0}\ge 0\). Therefore, by imposing that the derivative in (A.3) is nonnegative at \(L_i^*=\nu _i^*=0\), we obtain the following condition for the resulting optimal \(\mu ^*\):

$$\begin{aligned} \mu ^*\le 2 \left[ \partial P_i^{net}(R_i)/\partial R_i\right] _{R_i=0}\triangleq TH(i),\;\; \text{ at } \nu _i^*=L_i^*=0. \end{aligned}$$
(A.7)

Passing to consider the case of \(\nu _i^*=0\) and \(L_i^*\in ]0,\Delta f_i^*-L_b(i)[\), we observe that the corresponding KKT condition is unique, it is necessary and sufficient for the optimality and requires that (A.3) vanishes [52, chap.4]. Hence, the application of this condition leads to the following expression for the optimal \(L_i^*\) [see (A.3)]:

$$\begin{aligned} L_i^*\!=\!\frac{(T_t-\Delta )}{2}\!\left( \partial P_i^{net}(R_i)/\partial R_i\right) ^{-1}(\mu ^*/2),\quad \!\! \text{ at } \! \nu _i^*\!=\!0 \text{ and } 0<L_i^*<\left( \Delta f_i^*-L_b(i)\right) \!. \end{aligned}$$
(A.8)

Equation (A.8) vanishes at \(\mu ^*=TH(i)\) [see (A.7)] and this proves that the function: \(L_i^*(\mu ^*)\) vanishes at \(\mu ^*=\)TH(\(i\)). Therefore, since (A.7) already assures that vanishing \(L_i\) is optimal at \(\nu _i^*=0\) and \(\mu ^*\le \) TH(\(i\)), we conclude that the expression in (A.8) for the optimal \(L_i^*\) must hold when \(\nu _i^*=0\) and \(\mu ^*\ge \) TH(\(i\)). This structural property of the optimal scheduler allows us to merge (A.7), (A.8) into the following equivalent expression:

$$\begin{aligned} L_i^*=\frac{(T_t-\Delta )}{2}\left[ \left( \partial P_i^\mathrm{net}(R_i)/\partial R_i\right) ^{-1}(\mu ^*/2)\right] _+, \quad \text{ for } \nu _i^*=0, \end{aligned}$$
(A.9)

so that Equation (21b) directly arises from (A.5), (A.9). Finally, after observing that \(\nu _i^*\) cannot be negative by definition, from (A.6) we obtain (22). This completes the proof of Proposition 4.

Appendix B: Proof of Proposition 5

The reported proof exploits arguments based on the Lyapunov Theory which are similar, indeed, to those already used, for example, in [56, Sects. 3.4, 8.2], [13, Appendix II]. Specifically, after noting that the feasibility and strict convexity of the CPOP in (16) guarantees the existence and uniqueness of the equilibrium point of the iterates in (25) and (26), we note that Proposition 4 assures that, for any assigned \(\mu ^{(n)}\) and \(\left\{ L_i^{(n-1)}\right\} \), Eqs. (26a)–(26c) give the corresponding optimal values of the primal and dual variables \(\left\{ f_i^{(n)},L_i^{(n)},\nu _i^{(n)}\right\} \). Hence, it suffices to prove the global asymptotic convergence of the iteration in (25). To this end, after posing

$$\begin{aligned} U^{(n-1)}\left( \left\{ L_i^{(n-1)}\right\} \right) \equiv U^{(n-1)}\triangleq \left[ \sum _{i=1}^ML_i^{(n-1)}-L_\mathrm{tot}\right] ^2, \end{aligned}$$
(B.1)

we observe that \(U^{(n-1)}>0\) for \(\left\{ L_i^{(n-1)}\right\} \ne \left\{ L_i^{*}\right\} \) and \(U^{(n-1)}=0\) at the optimum, i.e., for \(\left\{ L_i^{(n-1)}\right\} = \left\{ L_i^{*}\right\} \) Footnote 4. Hence, since \(U^{(n-1)}(.)\) in (B.1) is also radially unbounded (that is, \(U^{(n-1)}(.)\rightarrow \infty \) as \(||\sum _{i=1}^M L_i^{(n-1)}-L_\mathrm{tot}||\rightarrow \infty \)), we conclude that (B.1) is an admissible Lyapunov’s function for the iterations in (25). Hence, after posing \(U^{(n)}\left( \left\{ L_i^{(n)}\right\} \right) =U^{(n)}\triangleq \left[ \sum _{i=1}^ML_i^{(n)}-L_\mathrm{tot}\right] ^2\), according to the Lyapunov’s Theorem [56, Sect. 3.10], we must prove that the following (sufficient) condition for the asymptotic global stability of (25) is met:

$$\begin{aligned} U^{(n)}<U^{(n-1)}, \quad \text{ for } n\rightarrow \infty . \end{aligned}$$
(B.2)

To this end, after assuming \(U^{(n-1)}>0\), let us consider, at first, the case of

$$\begin{aligned} \left( \sum _{i=1}^ML_i^{(n-1)}-L_\mathrm{tot}\right) >0. \end{aligned}$$
(B.3)

Hence, since \(\alpha ^{(n-1)}\) is positive, we have [see (25)]: \(\mu ^{(n)}<\mu ^{(n-1)}\), that, in turn, leads to [see (26c)]: \(L_i^{(n)}<L_i^{(n-1)}\), for any \(i=1,\ldots ,M\) Footnote 5. Therefore, to prove (B.2), it suffices to prove that the following inequality holds for large \(n\):

$$\begin{aligned} \left( \sum _{i=1}^M L_i^{(n)}-L_\mathrm{tot}\right) \ge 0. \end{aligned}$$
(B.4)

To this end, we observe that: (i) \(\left\{ \alpha {(n-1)}\right\} \) in (25) vanishes for \(n\rightarrow \infty \); and, (ii) \(L_i^{(n)}\) is limited up to \(\Delta f_i^{\max }\), for any \(i=1,\ldots ,M\) [see the constraints in (10b), (10d)]. As a consequence, the difference: \(\left( \mu ^{(n)}-\mu ^{(n-1)}\right) \) may be done vanishing as \(n\rightarrow \infty \). Hence, after noting that the functions in (25), (26) are continue by assumption, a direct application of the Sign Permanence Theorem guarantees that (B.4) holds when the difference in (B.3) is positive.

By duality, it is direct to prove that (B.2) is also met when the difference in (B.3) is negative. This completes the proof of Proposition 5.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cordeschi, N., Shojafar, M., Amendola, D. et al. Energy-efficient adaptive networked datacenters for the QoS support of real-time applications. J Supercomput 71, 448–478 (2015). https://doi.org/10.1007/s11227-014-1305-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11227-014-1305-8

Keywords

Navigation