Sleep to Stay Alive: Optimizing Reliability in Energy-Efficient Backbone Networks 1

Lavinia Amorosi,1 Luca Chiaraviglio,2 Paolo Dell’Olmo,1 Marco Listanti2 DSS Department, University of Rome Sapienza, Piazzale Aldo Moro 5, 00185 Rome, Italy 2 DIET Department, University of Rome Sapienza, Via Eudossiana 18, 00184 Rome, Italy Tel: (+39 0644585371), e-mail: [email protected]

ABSTRACT We consider the problem of extending device lifetime in backbone networks by exploiting sleep modes. In particular, when the device is put in sleep mode, its lifetime tends to increase. However, the transition between full power and sleep mode tends to decrease the lifetime. We model these two effects in an optimization problem, which considers the management of sleep modes in an operator network. Results, obtained on a realistic case study, show that the average lifetime of the devices in the network can be increased up to 43% compared to an always on solution. Keywords: energy-efficiency; reliability; lifetime models; sleep mode; backbone networks. 1. INTRODUCTION According to different studies, the energy consumption of the Information and Communication Technology (ICT) sector is far to be negligible, ranging between 2% to 10% of the global energy consumption [1], [2]. Among the different players in the ICT sector, telecom operators are experiencing huge electricity costs for powering on networking equipment. Focusing on backbone networks, network devices hardly scale their power with the actual load, resulting in a clear waste of energy when the load is below the maximum value. Starting from the seminal work of [3], different solutions have been proposed in order to reduce the network energy waste ([4], [5], [6], [7], [8] for detailed surveys). In this context, a widely considered approach to reduce the network energy waste is the exploitation of a sleep mode (SM) state to the network device. When a SM state is activated, most of device components are powered off. As a consequence, the traffic that was previously carried by the device has to be shift to other devices that remain powered on. In the context of backbone networks, this means to solve a multi-commodity problem with the goal of minimizing power consumption of active devices (i.e., not in SM) [9]. Even though the application of SM brings substantial energy savings [9], its impact on the device reliability is an open issue. In [10] authors have shown that SM-based approaches have an impact on the device lifetime. In particular, when a SM state is set, the lifetime of the device increases, due to the fact that the temperature of the device is lower compared to full power (i.e., all the components powered on). However, the transition between full power state and SM state may trigger a temperature variation, which on the contrary has a negative effect on the lifetime. Thus, there is clearly a tradeoff between the duration of SM and their frequency. In this context, an energy-aware solution maximizing the number of resources in SM in a given time period may not be beneficial for their lifetime. In fact, a longer duration of SMs may be surpassed by the penalties incurred when devices have to be powered on when traffic increases in the network. Thus, energy-aware approaches may even decrease the lifetime of the network devices, bringing to high reparation costs that could overcome the energy savings [10]. In this paper, we take into account both the above mentioned effects. In particular, we model the problem of maximizing the resources lifetime while exploiting SM. To the best of our knowledge, this problem has not been studied yet in the literature. In particular, preliminary results show that it is even possible to increase the device lifetime compared to an always on solution, while allowing some resources to be put in SM. Moreover, our model consider the linecards (LCs) of a backbone network, but it can be easily extended to other type of devices (e.g., routers, optical line amplifiers), paving the way for a sustainable and reliable network management. The rest of the paper is organized as follows. The model for LC lifetime is presented in Sec. 2. Sec. 3 reports the problem formulation. Results, obtained over a case study provided by an operator, are presented in Sec. 4. Finally, Sec. 5 concludes our work. 2. LINECARD LIFETIME MODEL We first review the model of [10], [11] to compute the lifetime. Here we report the main intuitions, while we refer the reader to [11] for the complete model. In particular, our focus is on LCs of a backbone network. The generic failure rate for a LC at full power is defined as γ on . When SM is applied to the LC, the new failure rate γ tot is defined as:   τs f tr τs tot on + γs + (1) γ =γ 1− T T NF |{z} | {z } Failure Rate Decrease

Failure Rate Increase

2

where τ s is the total time in SM during time period T , γ s is the failure rate in SM, f tr is the power switching rate between full power and SM, and N F is a parameter called number of cycles to failures. Thus, the total failure rate is composed by two terms: the first one tends to decrease the failure rate, while the second one has the opposite effect. In order to evaluate the lifetime increase/decrease w.r.t. the always on solution, we define a metric called Acceleration Factor (AF). It is to be observed that AF metric is lower than one if the LC lifetime is increased compared to the always on solution. On the contrary, a value higher than one means that the lifetime is decreased compared to the always on case. More formally, AF =

s γ tot s τ + = 1 − (1 − AF ) γ on {z T} | Lifetime Increase

γs γ on ,

χf tr |{z}

(2)

Lifetime Decrease

which is always lower than one since the failure rate in SM γ s (by neglecting where AF is defined as the negative effect due to power state transitions) is always lower than the failure at full power γ on . Moreover, χ is defined as γ on1N F , which acts as a weight for the power frequency rate f tr . The AF is then composed of two terms: the first one which tends to increase the lifetime (longer periods of SMs tends to increase this term which is negative), instead the second one tends to decrease the lifetime (the more often power state transitions occur, the higher this term will be). Moreover, the model is composed by parameters AF s and χ, which depend solely on the HW components used to build the device, while parameters τ s and f tr depend instead on the specific SM strategy. In the following, we detail the optimization model for minimizing the AF of a set of LCs. s

3. PROBLEM FORMULATION We consider an Internet Service Provider (ISP) network, where access nodes are sources and destinations of information and are connected to the ISP transport network. Transport nodes are neither sources nor destinations of traffic. We also assume that the links capacity and the traffic demand by all source/destination node pairs for each time period are given. Our objective is to find the set of routes and links that must be powered on so that the total AF of the network LCs is minimized, subject to flow conservation and maximum link utilization constraints. More formally, let G = (V, E) be the graph representing the network infrastructure. Let V be the set of the network nodes, while E the set of the network links. We assume | V |= N and | E |= L. Let ci,j > 0 be the capacity of the link (i, j) and α ∈ (0, 1] the maximum link utilization that can be tolerated. Let us denote as T the total amount of time under consideration. T is divided in time slots of period δt . Finally let ts,d (k) ≥ 0 be the traffic demand from node s to node d during slot k. s,d Focusing on the continuous variables, fi,j (k) ≥ 0 is the amount of flow from s to d that is routed through link (i, j) during slot k. Similarly, fi,j (k) ≥ 0 is the total amount of flow on link (i, j) during slot k. Moreover, s let us denote with τi,j ≥ 0 the total time in sleep mode of LC (i, j). Finally, let us denote with AFi,j ≥ 0 the AF for LC (i, j). In the following, we consider the integer variables. Let us denote with xi,j (k) a binary variable which takes value one if the LC (i, j) is powered on during slot k, zero otherwise. Moreover, let us denote with ξi,j (k) a binary variable which takes value one if LC (i, j) has experienced a power state transitions from slot k −1 to slot k, zero otherwise. Additionally, Ci,j ≥ 0 are integer variables counting the number of power state transitions for LC (i, j). Given the previous notation, our optimization problem can be formalized as follows: X 1 AF(i,j) (3) min ∗ L (i,j)∈E   tsd (k) if i = s X X s,d s,d −tsd (k) if i = d fi,j (k) − ∀i ∈ V ∀k (4) fj,i (k) =  0 if i 6= s, d j:(i,j)∈E j:(j,i)∈E X s,d fi,j (k) ∀(i, j) ∈ E ∀k (5) fi,j (k) = s,d

fi,j (k) ≤ α ∗ ci,j ∗ xi,j (k) xi,j (k) = xj,i (k) 

∀(i, j) ∈ E

∀(i, j) ∈ E

xi,j (k) − xi,j (k − 1) ≤ ξi,j (k) xi,j (k − 1) − xi,j (k) ≤ ξi,j (k)

∀k

(6)

∀k

∀(i, j) ∈ E

(7) ∀k

(8)

3

Figure 1: Orange-FT network topology.

Ci,j =

X

ξi,j (k)

∀(i, j) ∈ E

(9)

k

s τi,j =

X

(1 − xi,j (k)) ∗ δt

∀(i, j) ∈ E

(10)

k

s AFi,j = [1 − (1 − AF(i,j) )∗

s τi,j Ci,j + χ(i,j) ∗ ] T 2

∀(i, j) ∈ E

(11)

In this model we minimize the total AF of the LCs. Constraints (4) assure the flow conservation, constraints (5) evaluate the total flow routed on each link. Constraints (6) force the link load to be smaller than the maximum target utilization α, and also to power on the LC if the flow on the link is larger than zero. Constraints (7) impose bidirectionality. By means of constraints (8) we explain the variables ξi,j (k). Finally, constraints (9) count the number of power state transitions for each LC, while constraints (10) count the total time in SM for each LC. The last constraints (11) compute the variables AFi,j . The achieved formulation is a mixed integer linear programming (MILP) model. 4. RESULTS We solved our model on an instance of the Orange-FT network [12] composed of 38 nodes and 144 unidirectional links. The link capacities and the traffic of source/destination nodes are provided by the scenario. Moreover, traffic varies over a working day with a period of 24h. In particular, we have selected 6 slots with a duration of 4 hours each in the working day. Over such scenario we have solved the proposed optimization problem with Cplex 12.6 on a Windows machine Intel i3 3.5 GHz and 8GB of RAM. Tab. I reports the main results obtained s by varying the HW parameters AF(i,j) and χi,j . Each row in the table represents a different instance. In the first and second column are indicated the value of AF s and χ used. The third column shows the lower bound, the fourth the best solution found within the time limit and the fifth the percentage Gap calculated as the percentage difference between the objective and the lower bound. The last column shows the time limit that we have imposed in order to not exceed the maximum available memory. Focusing on the performance of the optimization problem, the results reported show a good behavior of the model. In particular, in all tests the percentage gap between the lower bound and objective can be considered small. Focusing then on the solutions obtained, we can clearly see that the resulting AF is constantly lower than one, meaning that with a lifetime-aware approach based on SM it is possible to even increase the device lifetime. In particular, the minimum AF is equal to nearly 0.56, meaning that a lifetime-aware solution can increase the lifetime of the network devices of 43% on average compared to an always on solution. This is an important indicator for operators, which should trigger the management lifetime-aware in current networks. Finally, the table reports also the variation of the HW parameters AF s and χ. As expected, both of them play a crucial role in determining the resulting AF. In particular, the lower is AF s , the lower is also the resulting AF, since the gain for putting in SM a LC is higher. However, the value of AF does not reach the value of AF s (even when χ is very small). This is due to the fact that different LCs have to be powered on in order to meet the traffic variation, and therefore it is not possible to put in SM all the resources. Moreover, we can see that also the frequency weight χ has an impact on the AF, since larger values of χ tends to increase the AF, due to the fact that power state transitions deteriorate the lifetime.

TABLE I: Optimization Results sleep AF(i,j) 0.2 0.2 0.2 0.5 0.5 0.5 0.8 0.8 0.8

χi,j 0.01 0.1 1 0.01 0.1 1 0.01 0.1 1

Lower Bound 0.5083 0.5112 0.5316 0.6905 0.6998 0.7076 0.8767 0.8810 0.8837

Objective 0.5633 0.5694 0.5555 0.7283 0.7291 0.7291 0.8923 0.8916 0.8888

Gap(%) 9.75 10.22 4.30 5.19 4.03 2.96 1.75 1.19 0.57

Time (minutes) 15 15 15 15 15 15 15 15 15

5. CONCLUSIONS We have proposed an optimization approach with the goal of minimizing the AF for a set of LCs of a backbone network. After formally defined the problem, we have solved it on a backbone operator network. Results show that both the HW and sleep mode parameters plays a crucial role for influencing the lifetime. In particular, we have shown that it is possible to increase up to 43% the lifetime of a network managing SM w.r.t. an always on solution. As next step, we will solve our problem on different network scenarios, considering also a longer period of time. Moreover, we plan to propose an incremental solution, which does not assume the knowledge of future traffic. ACKNOWLEDGMENTS The research leading to these results has received funding from the Sapienza Awards LIFETEL. REFERENCES [1] Global e-Sustainibility Initiative (GeSI), “SMART 2020: Enabling the Low Carbon Economy in the Information Age,” http://www.theclimategroup.org/assets/resources/publications/ Smart2020Report.pdf. [2] W. Van Heddeghem, S. Lambert, B. Lannoo, D. Colle, M. Pickavet, P. Demeester, “Trends in Worldwide ICT Electricity Consumption from 2007 to 2012”, Elsevier Computer Communications, vol. 50, pp.64-76, September 2014. [3] M. Gupta and S. Singh, “Greening of the Internet,” Proc. of ACM SIGCOMM, Karlsruhe, Germany, August 2003. [4] Y. Zhang, P. Chowdhury, M. Tornatore, and B. Mukherjee, “Energy Efficiency in Telecom Optical Networks,” IEEE Communications Surveys & Tutorials, vol. 12, no. 4, pp. 441–458, 2010. [5] R. Bolla, R. Bruschi, F. Davoli, and F. Cucchietti, “Energy Efficiency in the Future Internet: a Survey of Existing Approaches and Trends in Energy-aware Fixed Network Infrastructures,” IEEE Communications Surveys & Tutorials, vol. 13, no. 2, pp. 223244, 2011. [6] R. Bolla, F. Davoli, R. Bruschi, K. Christensen, F. Cuchietti, and S. Singh, “The Potential Impact of Green Technologies in Next-generation Wireline Networks: Is There Room for Energy Saving Optimization?” IEEE Communications Magazine, vol. 49, no. 8, pp. 80–86, August 2011. [7] W. Van Heddeghem, B. Lannoo, D. Colle, M. Pickavet, and P. Demeester, “A Quantitative Survey of the Power Saving Potential in IP-over-WDM Backbone Networks,” IEEE Communications Surveys & Tutorials, 2014. [8] M. N. Dharmaweera, R. Parthiban, and Y. A. Sekercioglu, “Towards a Power-efficient Backbone Network: The State of Research,” IEEE Communications Surveys & Tutorials, vol. 17, no. 1, pp. 198-227 2015. [9] L. Chiaraviglio, M. Mellia, and F. Neri, “Minimizing ISP Network Energy Cost: Formulation and Solutions,” IEEE/ACM Transactions on Networking, vol. 20, no. 2, pp. 463476, April 2012. [10] L. Chiaraviglio, P. Wiatr, P. Monti, J. Chen, J. Lorincz, F. Idzikowski, M. Listanti, and L. Wosinska, “Is Green Networking Beneficial in Terms of Device Lifetime?,” IEEE Communications Magazine. to appear, 2015. [11] L. Chiaraviglio, P. Wiatr, P. Monti, J. Chen, L. Wosinska, J. Lorincz, F. Idzikowski, M. Listanti, “Impact of Energy-efficient Techniques on a Device Lifetime,”, Proc. of IEEE Online GreenComm, online conference, November 2014. [12] F. Idzikowski, L. Chiaraviglio, R. Duque, F. Jimenez, and E. Le Rouzic, “Green Horizon: Looking at Backbone Networks in 2020 from the Perspective of Network Operators,” in Proc. of IEEE ICC, Budapest, Hungary, June 2013.