Optimal Sustainable Management of 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 optimally formulate the problem of maximizing the sustainability in a backbone network, with the goal of balancing network energy savings, device fixing costs, and users utility. Results show that the proposed solution is able to increase the operator revenue, while both a classical energy-saving approach and an always on solution tend to increase the operator costs. Keywords: backbone networks; total sustainability; costs/revenues trade-offs 1. INTRODUCTION The explosive growth of bandwidth demand has imposed operators to deploy high-performing and powerhungry network devices in the last years. As a result, the electricity consumption of the whole Information and Communication Technology Sector (ICT) has been constantly increased (see e.g., [1]). More in depth, telecom operators are facing huge electricity costs in order to keep their devices always powered on to serve the users. One of the possible ways to reduce the costs paid by large telecom providers is the exploitation of energyefficient approaches [2]. Among them, the application of a sleep mode approach allows to put the device in a low power consumption state (typically for minutes or hours), and to concentrate the user traffic on (possibly few) devices that remain powered on. As a consequence, the associated electricity bill is reduced thanks to the fact that the number of powered on devices follows an almost periodic trend (i.e., few devices powered on during the night, and then most of devices kept at full power during the day). Even though the reduction of costs in terms of energy brought by sleep mode approaches has been already recognized and accepted by the research community, little efforts have been performed so far to understanding what are the implications of adopting this type of solution in an operator network. In particular, the transition between sleep mode and full power, applied regularly to the devices in a network, may dramatically reduce their lifetime [3]. When the devices decrease their lifetime, they need to be fixed more frequently, thus increasing the associated reparation/replacement costs [4]. As a result, there is a trade-off between the amount of energy that can be saved in a network and the maximum admissible lifetime degradation [5]. Additionally, another effect that has to be considered when adopting energy-efficient solutions is the impact on the Quality of Service (QoS) to users. More in depth, if users are served by few network devices, their experienced QoS may be lower compared to the case in which all devices are always powered on. A user experiencing a low QoS may then decide to migrate to another operator, thus again representing a loss for its original operator. In this context, a natural question arises: Is it possible to trade between network energy savings, device fixing costs, and user QoS in a backbone network? The answer to this question is the goal of this paper. In particular, we express the total sustainability of a backbone network as a metric encompassing electricity costs, lifetime costs and users QoS. We then optimally formulate the problem of maximizing the sustainability in a backbone network. To the best of our knowledge, this is the first work investigating this aspect in a backbone network. Results, obtained over a representative scenario, clearly show that targeting the total sustainability triggers revenues for the operator. On the contrary, solutions targeting only the maximization of the energy-savings, or maximization of the users QoS (i.e., by keeping all the devices always powered on), tend to reduce the sustainability. We believe that this work is a first step towards a more comprehensive approach which should take into account all the costs/revenues managed by the operator when energy-efficient policies are applied. More in depth, we call for in-depth measurements for precisely estimating the fixing costs in a backbone operator. This task could also lead to the definition of new failure models linked to energy-efficient approaches. Additionally, we plan also to deeply study the tariff plans of the users, and to link them with the total costs for managing the network. The rest of the paper is organized as follows. The optimal formulation to maximize the total sustainability in a backbone network is proposed in Sec. 2. The scenario description and the parameters settings are described in Sec. 3. Results are detailed in Sec. 4. Finally, Sec. 5 concludes our work. 2. PROBLEM FORMULATION We consider a backbone network composed of source/destination nodes and purely transport nodes. 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 maximize the total sustainability of the network, by jointly considering the users utility, the device fixing costs, and the network energy costs. More in depth, the users utility is defined as a revenue for the operator to serve users at a given
2
rate. The higher is the rate for serving users, the higher is also their utility. In this way, we also take into account the QoS for serving the users. By assuming that time is divided in time slots of fixed duration, we target the maximization of the sustainability for each time slot by acting on the the power state of each LineCard (LC) in the topology. Each LC can be at full power or in sleep mode (SM). 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. We assume that the total period of time under consideration is divided in time slots of duration δt . Let us denote with k the current time slot index. We then introduce the constraints of our problem. Focusing on traffic, we assume a variable amount of traffic for each source s and each destination d. Let tsd min (k) be the minimum amount of traffic for node pair s-d at time slot k. Similarly, let tsd max (k) be the maximum amount of traffic between s and d at time slot k. Let us denote with continuous variables λsd (k) the actual amount of traffic assigned to pair s-d at k. Additionally, s,d (k) ≥ 0 is the amount of flow from s to d that is routed through link (i, j) during current time slot. fi,j Similarly, fi,j (k) ≥ 0 is the total amount of flow on link (i, j) during slot k. Given the previous definitions, we first impose that traffic has to be routed in the network: λsd (k) if i = s X X s,d s,d −λsd (k) if i = d fi,j (k) − fj,i (k) = ∀i ∈ V [Gbps] (1) 0 if i 6= s, d j:(i,j)∈E j:(j,i)∈E We also impose the constraints on the variable λsd (k): λsd (k) ≤ tsd max (k) ∀(s, d) ∈ E sd
λ (k) ≥
tsd min (k)
∀(s, d) ∈ E
In the next step, we compute the total amount of flow on each link: X s,d fi,j (k) = fi,j (k) ∀(i, j) ∈ E
[Gbps]
(2)
[Gbps]
(3)
[Gbps]
(4)
s,d
We then limit the total amount of flow to be smaller than the link capacity: fi,j (k) ≤ αci,j xi,j (k) ∀(i, j) ∈ E
[Gbps]
(5)
where xi,j (k) a binary variable which takes value one if the LC (i, j) is powered on during slot k, zero otherwise. We then consider the users utility. Let us denote with Umin and Umax a minimum and a maximum utility sd sd value, respectively. Moreover, let us denote with λsd min and λmax minimum and maximum thresholds for λ (k). The resulting utility variable Us,d for users requesting traffic from node s to node d is then computed as: sd sd Umin if λ (k) ≤ λmin sd sd λ (k)−λmin sd sd (6) Us,d = Umin + (Umax − Umin ) log2 1 + λsd −λsd if λsd [USD] min < λ (k) ≤ λmax max min U if λsd (k) ≥ λsd max
max
The previous expression assumes that the user utility scales logarithmically with the actual amount of served traffic λsd (k). In this way, we tend to reward the increment of users utility experienced at lower rates. The total utility variable Utot (k) at time slot k is then computed as: X Utot (k) = Us,d + Utot (k − 1) [USD] (7) s,d
where Utot (k − 1) is an input parameter representing the utility at previous time slot. In the following, we focus on the energy costs. We first impose the fact that, if LC (i, j) is put in SM, also LC (j, i) has to be powered off: xi,j (k) = xj,i (k) ∀(i, j) ∈ E (8) We then compute the total energy cost at time slot CE (k) k X CE (k) = cKW h δt xi,j (k)Pi,j + CE (k − 1) [USD]
(9)
i,j
where cKW h is the hourly electricity cost, Pi,j is the power consumption of LC (i, j) when it is powered on, and CE (k − 1) is the energy cost at previous time slot. Note that the only variables in the previous equation are CE (k) and xi,j (k), while cKW h , δt , Pi,j and CE (k − 1) are input parameters.
3
Finally, we focus on the fixing costs, by adopting the same failure model of [3]. 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. ξi,j (k) can be set by the following constraint: xi,j (k) − xi,j (k − 1) ≤ ξi,j (k) ∀(i, j) ∈ E (10) xi,j (k − 1) − xi,j (k) ≤ ξi,j (k) Moreover, let Ri,j (k) ≥ 0 be integer variables counting the number of power state transitions for LC (i, j) up to time slot k. Ri,j (k) = ξi,j (k) + Ri,j (k − 1) ∀(i, j) ∈ E (11) where Ri,j (k − 1) is an input parameters storing the number of transitions up to previous time slot. Additionally, we introduce the continuous variable τi,j (k), which stores the total amount of time in SM for LC (i, j) up to time slot k: τi,j (k) = (1 − xi,j (k))δt + τi,j (k − 1) ∀(i, j) ∈ E [h] (12) where τi,j (k − 1) is the total time in SM for LC (i, j) up to previous time slot. Given the number of transitions Ri,j (k) and the total time in SM τi,j (k − 1) we then compute the AF for LC (i, j) at time slot k. The AF is a metric introduced in [3] expressing the current lifetime normalized over the lifetime assuming that the LC is always powered on. More formally: Ri,j (k) τi,j (k) s + χ(i,j) ∀(i, j) ∈ E (13) AFi,j (k) = 1 − (1 − AF(i,j) ) T (k) 2 s where AF(i,j) and χ(i,j) are hardware input parameters, and T (k) is the amount of time from the first time slot to time slot k. The total fixing costs CR (k) at time slot k are then computed as: X on CR (k) = Cr δt AFi,j (k)θi,j + CR (k − 1) [USD] (14) i,j on where Cr is the hourly cost for fixing a LC, θi,j is the failure rate for LC always powered on, and CR (k − 1) are the fixing costs up to previous time slot. Given the previous constraints, our goal is then to maximize the total sustainability of the system:
max [Utot (k) − CE (k) − CR (k)]
[USD]
(15)
3. SCENARIO AND PARAMETERS SETTINGS We consider the backbone scenario of [5], [6]. The network is composed of 38 nodes and 72 bidirectional links. Additionally, the traffic between each node pair and the amount of capacity installed on each link are provided in the scenario. The network is dimensioned to satisfy a maximum link utilization equal to 50% of the link capacity (during the peak hour). Moreover, the information about variation of traffic over time is also provided. More in depth, we consider a daily traffic profile (which is repeated across a set of 20 days), and a time slot granularity of 4 hours, i.e., there are 6 time slots in a day. Focusing on power consumption, we have adopted the same model of [5] in which each link consumes an amount of power corresponding to a pair of optical transponders and a pair of IP interface ports. Each 10 Gbps transponder consumes 37 W and each 1 Gbps port consumes 10 W. Moreover, we assume that the power consumption of a link is negligible, when it is put in in sleep mode. Finally, we assume a cost of electricity cKW h equal to 0.16 [USD/kWh] [3]. In the following, we have considered the parameters related to the fixing costs. More in depth, following the s same intuitions of [3], we have set AF(i,j) =0.5, since we assume that the lifetime when the device is in SM is doubled compared to the case in which it is always powered on. Focusing then on the other hardware parameter χ(i,j) , we have initially set χ(i,j) =0.001. Recall that this parameter acts as a weight for the number of power state transitions. With this setting, we have assumed that the impact of power state transition is not so high, i.e., the device can sustain hundreds of transitions before introducing a significative lifetime decrease. Additionally, on the failure rate for LC always powered on θi,j is set to 1/87600 [1/h] [3], which corresponds to a lifetime equal to 10 years. Finally, the fixing cost is equal to 190 kUSD in accordance to [3]. sd Focusing then on the user utility, we have set λsd min = 0.0003 Gbps ∀s, d, λmax = 2.92 Gbps ∀s, d, Umin = 0.033 USD and Umax = 114 USD, respectively. With this setting, the users utility is larger than the energy costs during the peak hour (which justifies the deployment of the network), while it is lower than the energy costs during the off-peak hour and with all the LCs powered on (which justifies the application of energy-saving techniques).
Total Sustainability [USD]
Total Sustainability [USD]
150000 100000 50000 0 -50000 -100000 -150000 -200000 -250000 -300000
All Sustainability Only Energy Costs Only Users Utility 0
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8 10 12 Time [day]
(a) χ = 0.001
14
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100000 0 -100000 -200000 -300000 -400000 -500000 -600000 -700000
All Sustainability Only Energy Costs Only Users Utility 0
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8 10 12 Time [day]
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(b) χ = 0.1
Figure 1: Comparison between the formulation targeting the sustainability against the one targeting only energycosts and the one targeting only the users utility. 4. RESULTS We have then run the sustainable formulation of Sec. 2 over the considered scenario and parameters set. Moreover, we have considered the following comparisons: i) only minimization of energy costs (i.e., a classical energysaving approach), and ii) only maximization of users utility (i.e., a solution in which all devices are always powered on). In these two latter cases, the total sustainability is then computed off-line at the end of the optimization process. Fig. 1(a) reports the sustainability vs. time for the three formulations. Interestingly, the minimization of energy-costs tends to decrease the sustainability, i.e., at the end of the considered 20 days period the total sustainability is negative, meaning that the operator has paid a high cost rather than achieving a revenue. This is due to two main reasons: i) the lifetime degradation triggered by frequent full power / sleep mode transitions, and ii) the fact that the revenue for serving the users is not considered. Moreover, the maximization of users utility tends to have an almost constant and negative sustainability. This is due to the fact that this solution does not consider the energy costs, resulting in an electricity waste. Finally, our proposed approach, targeting the whole sustainability (i.e., users utility, device fixing costs, and energy costs), always brings a revenue for the operator, resulting in a final sustainability of more than 150000 USD. In the following, we have then investigated the impact of increasing the fixing costs, by setting a value of χ = 0.1. Recall that χ is an hardware parameter acting as a weight for power state transitions in Eq. 13, thus potentially increasing the impact of fixing costs. In this case, the minimization of energy costs tends to notably decrease the sustainability at the end of the 20 days period. Clearly, the formulation targeting the maximization of users utility is not influenced by χ, since no transitions are introduced. Finally, the maximization of total sustainability tends to achieves revenues also in this case. This is due to the fact that the fixing costs, the users utility and the energy costs are jointly taken into account. 5. CONCLUSIONS AND FUTURE WORKS We have optimally formulated the problem of maximizing the total sustainability in a backbone network. Our sustainability metric jointly takes into account the users utility, the device fixing costs, and the network energy costs. We have evaluated our solution in backbone scenario, showing that the proposed formulation outperforms both a classical approach based on the maximization of energy savings and a solution always maximizing the users utility. As next step, we plan to validate the proposed failure rate model with real devices, as well as to propose more detailed costs models driven by operator feedback. ACKNOWLEDGMENTS The research leading to these results has received funding from the Sapienza Awards DIAMETER. REFERENCES [1] W. Van Heddeghem, et al., “Trends in Worldwide ICT Electricity Consumption from 2007 to 2012”, Elsevier Computer Communications, vol. 50, pp.64-76, September 2014. [2] F. Idzikowski, et al., “A Survey on Energy-Aware Design and Operation of Core Networks,” IEEE Communications Surveys and Tutorials, on press, 2015. [3] L. Chiaraviglio, et al., “Is Green Networking Beneficial in Terms of Device Lifetime?,” IEEE Communications Magazine, vol. 53, n. 5, pp. 232-240, 2015. [4] P. Wiatr, et al., “Energy Efficiency Versus Reliability Performance in Optical Backbone Networks,” Journal of Optical Communications and Networking, Vol. 7, N. 3, pp. 482-491, 2015. [5] L. Chiaraviglio, et al., “LIFETEL: Managing the Energy-Lifetime Trade-off in Telecommunication Networks,” IEEE Communications Magazine, on press, 2016. [6] F. Idzikowski, et al., “Green horizon: Looking at backbone networks in 2020 from the perspective of network operators,” IEEE ICC, Budapest, Hungary, June 2013.
