Lifetime Awareness in Backbone Networks with Sleep Modes Luca Chiaraviglio, Antonio Cianfrani, Marco Listanti, Marco Polverini DIET Department, University of Rome Sapienza, Rome, Italy, email {name.surname}@uniroma1.it Abstract—We investigate the problem of managing the lifetime of links in IP backbone networks exploiting a sleep mode (SM) state. In particular, the SM duration tends to increase the lifetime, while the frequency of power state transitions tends to decrease it. After optimally formulating the problem of limiting the impact on the link lifetime when SMs are applied, we propose an online heuristic, called AFA, to practically solve it. Our solution performs SMs decisions at each time slot, without requiring the knowledge of future traffic (which may be an unrealistic assumption). We test the performance of AFA on a realistic case study, by comparing it against two algorithms energy-aware. Results show that AFA outperforms the other algorithms in terms of lifetime performance, while allowing devices to be put in SMs.

I.

I NTRODUCTION

In the last years, the problem of energy-efficient backbone networks has been deeply investigated in the literature, starting from the seminal work of [1]. Among the different solutions proposed to save energy in backbone networks, the exploitation of a SM state is a promising approach. When a SM state is set for a device in a backbone network, the other devices that remain powered on have to sustain the traffic between source and destination nodes. In this context, different works (see for example [2], [3], [4], [5]) have investigated the management of IP backbone networks by adopting sleep modes (SMs). The main outcome of these works is that networks with SM capabilities are able to save a consistent amount of energy, due to the fact that the traffic experiences high fluctuations between the day and the night, resulting in a large number of resources that can be put in SMs during off peak hours. However, the impact of SMs on the reliability of network devices is an open issue [6], [7]. In particular, there are two opposite effects influencing the lifetime of network devices [8]: the duration of SMs, which tends to increase the lifetime, and the change in the power state (from SM to full power and vice-versa), which instead decreases the lifetime. As an example, in [9] authors perform temperature measurements for different HardWare (HW) components in a data-center, showing a sharp increase in the failure rate when power state changes are applied. In general, when a network device experiences a failure, the traffic flowing on the device may be dropped, resulting in a Quality of Service (QoS) degradation for users. Additionally, reparation costs are incurred, which may involve even the replacement of the whole device. In particular, the reparation costs may even exceed the monetary savings derived from SMs [10]. All these facts suggest that the device lifetime plays a crucial role in determining the efficiency of SMs, suggesting

that the energy saving may be not the only metric to prove the effectiveness of a SM-based approach. The problem of the interplay between SM and device lifetime has been initially advocated in [11] for IP backbone networks and then extended in [12] also for cellular networks. More in depth, in [11] we have proposed a simple model to evaluate the lifetime increase/decrease of network devices taking into account the duration of SMs and their frequency. The model shows that energy-aware algorithms have an impact on the device lifetime, which may be positive or negative, depending on the HW components used to build the device and on the adopted strategy to choose which devices to put in SM. However, the considered time period for the evaluation of the impact on the lifetime, i.e, a single day, is not comprehensive, and it could hide the effects of a long-term evaluation, i.e., several days. In this context, some natural questions arise, like: Is it possible to build an algorithm exploiting SMs which always limits the impact on the lifetime? What is the impact of SMs in the long-term? The answer to these questions is the goal of the paper. In particular, we go four steps further w.r.t. previous works by: i) considering the evolution of the lifetime over different days, ii) optimally formulating the problem, iii) providing an energy-aware heuristic that accounts for the device lifetime, iv) evaluating our solution against two algorithms which instead target solely the energy consumption. To the best of our knowledge, none of the previous works have investigated these issues. Moreover, our solution, called Acceleration Factor Algorithm (AFA), performs SM decisions for the devices at each traffic variation, without requiring the knowledge of future traffic (which may be an unrealistic assumption). Our preliminary results show that AFA, which considers the lifetime during the SM decision, is able to efficiently manage the interplay between the lifetime and the power consumption of network devices. Thus, we argue that an energy-aware management should be pursued only when the lifetime is taken into account, paving the way for a sustainable and reliable Internet. The rest of the paper is organized as follows. The model adopted for evaluating the device lifetime is presented in Sec. II. Sec. III reports the optimal formulation. Our heuristic lifetime-aware is described in Sec. IV. Heuristic results obtained over a realistic case study are reported in Sec. V. Finally, Sec. VI concludes our work. II.

M ODELING THE D EVICE L IFETIME

We first review the model of [7], [8] to compute the lifetime. Here we report the main intuitions, while we refer the

reader to [8] for the complete model. In particular, our focus is on links of a IP backbone network. The generic failure rate for a link at full power is denoted with γ on . When SM is applied to the link, the new failure rate γ tot is defined as:   τs τs f tr γ tot = γ on 1 − + γs + (1) T T} NF |{z} | {z | {z } On Failure Rate

SM Failure Rate

Transition Failure Rate

in the network for each time slot:  

tsd (k) if i = s −tsd (k) if i = d  0 if i = 6 s, d j:(i,j)∈E j:(j,i)∈E (4) s,d where fi,j (k) ≥ 0 is the amount of flow from s to d that is routed through link (i, j) during slot k. X

s,d fi,j (k)−

X

s,d fj,i (k) =

where τ s is the total time in SM during time period T , γ s is the failure rate in SM (which is supposed to be lower than γ on ), f tr is the power switching rate between full power and SM, and N F is a parameter called number of cycles to failures.

We then compute the total amount of flow fi,j (k) ≥ 0 on each link for each slot: X s,d fi,j (k) = fi,j (k) (5)

In order to evaluate the lifetime increase/decrease w.r.t. the always on solution, we define a metric called acceleration factor (AF) [7]. The AF metric is lower than one if the link lifetime is increased compared to the always on solution. On the contrary, a value larger than one means that the lifetime is decreased compared to the always on case. More formally,

Let ci,j > 0 be the capacity of the link (i, j) and α ∈ (0, 1] be the maximum link utilization that can be tolerated, respectively. Moreover, we introduce the binary variable xi,j (k), which takes value one if link (i, j) is powered on during slot k, zero otherwise. The total amount of flow should be smaller than ci,j , scaled by α:

AF =

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

χf tr |{z}

(2)

Lifetime Decrease

where AF s is defined as γγon , which is always lower than one since the failure rate in SM γ s (by neglecting 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 by two terms: the first one which tends to increase the lifetime (longer periods of SMs tends to increase this term which is negative), while the second one instead tends to decrease the lifetime (the more often power state transition occur, the higher will be this term). Moreover, the model is composed by parameters AF s and χ, which depend solely on the HW components used to build the link, while parameters τ s and f tr depend instead on the realization of SM. In the following, we detail the optimal formulation for minimizing the AF of a set of network links. III.

O PTIMAL F ORMULATION

Our goal is to minimize the AF in a network by exploting SM. An informal description of our problem is the following: Given the set of nodes and links in the network, the traffic for each time slot, Minimize the average AF over the whole time period, Subject to connectivity and maximum link utilization for each time slot. More formally, let G = (V, E) be the network topology. Let V be the set of the network nodes, while E the set of network links, being | V |= N and | E |= L. Let us denote with T the total amount of time under consideration. T is divided in K time slots of period δt . Moreover, let ts,d (k) ≥ 0 be the traffic demand from node s to node d during slot k. Our goal is to minimize the average AF of the links in the network: 1 X min AF(i,j) (3) L

s,d

fi,j (k) ≤ αci,j xi,j (k)

(6)

Note that with this constraint we impose also the fact that a link has to be powered on if the flow on it is larger than zero. The link state has to be the same in both directions: xi,j (k) = xj,i (k)

(7)

We then introduce the binary variable zi,j (k), which takes value one if link (i, j) has experienced a power state transition from slot k − 1 to slot k, zero otherwise. The value of zi,j (k) is set with the following two constraints:  xi,j (k) − xi,j (k − 1) ≤ zi,j (k) (8) xi,j (k − 1) − xi,j (k) ≤ zi,j (k) We then introduce the variable Ci,j ≥ 0, which counts the total number of transitions for each link during the whole time period: K X zi,j (k) (9) Ci,j = k=1

s Additionally, we introduce the variable τi,j ≥ 0, which instead computes the total time in SM for each link: s τi,j =

K X

[1 − xi,j (k)]δt

(10)

k=1

Finally, we introduce the variable AFi,j ≥ 0 to compute the total AF for each link:    τs  Ci,j i,j s AFi,j = 1 − 1 − AF(i,j) (11) + χ(i,j) T 2 The factor two that divides Ci,j is introduced because a power cycle is always composed by at least two transitions (i.e., from full power to SM, and then from SM to full power).

(i,j)∈E

The presented formulation falls in the class of NP-hard problems,1 which may be very difficult to be solved in

However, the objective can be pursued only under different constraints. In particular, we impose that traffic has to be routed

1 The problem falls in the class of multi-period multi-commodity capacitated flow problems with integer costs.

practice. Moreover, the optimization problem requires the full knowledge of traffic over the whole time period T , which may be an unrealistic assumption. To overcome both the two aforementioned issues, we have decided to follow an on-line approach,2 which is able to solve the problem incrementally, i.e., without requiring the knowledge of future traffic. In the following section, we detail our heuristic. IV.

T HE AFA A LGORITHM

We develop a new heuristic, called Acceleration Factor Algorithm (AFA). In particular, we take SM or power on decisions at every traffic change, while considering the values of the current AFs. The key intuition of the AFA algorithm is to compute incrementally the AFs, without assuming the knowledge of future traffic as well as of future power state transitions. Therefore, rather than working on the entire time period T , AFA takes decisions (in terms of links put in SM or powered on) at each time slot k, considering only the state of links up to k − 1 and the traffic at slot k. Alg. 1 reports the AFA pseudocode. The algorithm requires as input parameters the current time slot index k, the current traffic matrix, the link capacities and the links state (powered on or in SM for all time slots until k − 1). The links states are stored in a matrix of size L × K. Each entry stores the state of the link at given time slot: zero if the link in SM, one otherwise. Initially, the current state of links is taken from previous time slots (line 1).3 Then, the AF metric is computed for each IP link, as well as the average AF (lines 2-3). This computation takes into account the time slots up to k − 1. Then, the links are sorted with decreasing AF values (line 4).4 Initially, the links are selectively powered on until the maximum link utilization is not satisfied (lines 5-17). In particular, the current traffic is flown on the set of links (line 5). If the maximum link utilization constraint is violated (line 6), the algorithm searches for candidates links to be powered on. The first links to be powered on are the ones in SM which have also the highest AF (lines 7-8). The intuition is that these links have been used frequently in the past (due to the fact that they have the largest AF values), therefore they may be able to satisfy the current traffic. This procedure continues until the maximum link utilization constraint is not satisfied. In the following, the algorithm looks for candidate links to put in SM (lines 18-37). In order to limit the transitions introduced (and consequently the increase of the AF), the SM procedure is activated only if the average AF is between two thresholds, denoted as δl and δh , respectively (line 18). The intuition is two-fold. On one side, if the average AF is low, it is not useful to look for other links to be put in SM, since these switch offs will trigger transitions likely worsening the average AF. On the other side, if the average AF is high, it might not be convenient to trigger SM, since different transitions have taken place in the past (likely due to a traffic increase). Thus, the algorithm activates SM only if the average AF is between the two thresholds. By imposing different values of δl and δh , 2 Due to the problem complexity, we will not present results from the optimal formulation. However, we believe that the presented formulation is useful to understand the problem. 3 For the iteration k = 1 all links are assumed to be at full power. 4 We have tested also an increasing sorting. However, the best results are obtained with a decreasing one.

Algorithm 1 Pseudo-code description of the AFA algorithm. Input: current time slot index k, current traffic matrix trf m, link capacities cap, state of links links s from 1 to k − 1, Output: updated state of links links s at k 1: links s[1 : L,k]=links s[1 : L,k − 1]; 2: AF array=compute AF(links s[1 : L,1 : k]); 3: AF mean=compute AF mean(AF array); 4: sorted l=sort AF(AF array, order type); 5: links flow = compute lf(trf m, links s[1 : L,k]); 6: if (check max util(links flow, cap) == false) then 7: for e = 1; e ≤num links; e++ do 8: if (sorted l[e].state == SM) then 9: // enable links until maximum link utilization is not satisfied 10: links s[sorted l[e],k]=1; 11: links flow = compute lf(trf m, links s[1 : L,k]); 12: if (check max util(links flow, cap) == true) then 13: break; 14: end if 15: end if 16: end for 17: end if 18: if (AF mean≥ δl ) && (AF mean≤ δh ) then 19: for e = 1; e ≤num links; e++ do 20: if (sorted l[e].state == ON) then 21: if (AF array[sorted l[e]]≥ γl ) && (AF array[sorted l[e]]≤ γh ) then 22: // put the current link in SM 23: links s[sorted l[e],k]=0; 24: if (check connectivity(links s[1 : L,k]) == false) then 25: // enable link if connectivity is not satisfied 26: links s[sorted l[e],k]=1; 27: else 28: links flow = compute lf(trf m, links s[1 : L,k]); 29: if (check max util(links flow, cap) == false) then 30: // enable link if maximum link utilization is not satisfied 31: links s[sorted l[e],k]=1; 32: end if 33: end if 34: end if 35: end if 36: end for 37: end if

the behavior of the algorithm is varied. In particular, if δl = 0 and δh >> 1, the algorithm will always try to put in SM network links, thus acting like an energy-aware algorithm. On the contrary if δl > 0 and δh ≈ 1 the algorithm will apply SMs less often compared to an energy-aware algorithm. In the following step, the single links are considered to be put in SM (line 19). More in depth, the algorithm compares the AF of the links powered on against other two thresholds, denoted as γl and γh , respectively (line 21). The rational of such thresholds is to have another degree of freedom in choosing the set of candidates links to be put in SM, by considering the AF of the single links. This is due to the fact that the AF of the single links may differ from the average [7], with some links having high values of AF while other links having low ones. Moreover, both γl and γh can take different values than δl and δh . If both the thresholds are verified, then the current link is put in SM (line 23). Then, a connectivity check is performed (line 24), i.e., to verify that the subgraph of links without the

O RANGE -FT N ETWORK C HARACTERISTICS

Parameter Type Number of Nodes Number of Links Average Degree Routing Weights Routing Algorithm Maximum Link Utilization Traffic Granularity

1.2

Setting/Value Core Level 38 72 3.78 Provided by Operator Shortest Path 50% 1 hour

1.1

Average AF

TABLE I.

1 0.9 0.8 0.7

current link is still connected. If the connectivity check is not satisfied, the current link is put again at full power. Otherwise, the link flow is computed (line 28) and the maximum link utilization constraint if verified (line 29). If the condition is not satisfied, the current link is put at full power (line 31), otherwise it is left in SM.5 V.

P ERFORMANCE E VALUATION

We implemented AFA on a custom simulator6 and we have tested it on a realistic case-study. In particular, we have considered the reference scenario provided by Orange-FT [13]. Tab. I reports the main network characteristics. We refer to reader to [14] for a detailed description of this scenario. In brief, the operator has provided the topology in terms of nodes and links, link capacities, routing weights, and the traffic variation over one working day, with a time granularity of one hour between one traffic matrix and the following one. Moreover, the maximum link utilization is set to 50% of the link capacity, as suggested by the operator. Focusing on power consumption, we have adopted the same model of [15], 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 37W and each 1 Gbps port consumes 10W. Finally, we assume that when a link is in sleep mode, the power consumption is negligible. Unless otherwise specified, we have considered a time period T equal to 15 days. In particular, we have assumed that the 24h traffic profile provided by the operator is repeated over the days. This is a conservative assumption, since traffic during weekends may be lower compared to working days. However, we believe that the obtained results are representative. We have assumed the same HW parameters for the links, i.e., all links are deployed with similar devices in terms of HW characteristics. Moreover, we have initially set the HW parameters AFijs = 0.2 and χij = 0.5 [1/h], respectively. Recall that AFijs is the AF of the device when a SM state is applied (without considering transitions), while χij is the weight for the frequency of power state changes. The ratio for this setting is the following. With a low AFijs the gain for putting the link in SM is high, since its lifetime is increased up to a factor of five compared to the always on solution. However, we always weigh the frequency of transitions with a value of χij = 0.5 [1/h] that tends to decrease the lifetime in the long-term. Due to the fact that measurements of AFijs and χij values are not yet available in the literature, we have also 5 In the presented approach, the routing may change between one time slot and the following one, thus introducing potential Quality of Service degradation for users. We leave the evaluation of this aspect as future work. 6 We have coded AFA on a standard simulator that performs shortest path routing over a topology with the possibility of putting in SM a subset of links. Thus, we believe that the presented results can be easily reproduced.

0.6

δl=0 δh=1 δl=0 δh=1.5 δl=0.6 δh=0.8 δl=0.4 δh=0.9 δl=0.6 δh=0.9 δl=0.6 δh=1.0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Time [day]

Fig. 1.

AF variation vs. time: δh and δl tuning.

performed in the last part of our work a sensitivity analysis w.r.t. both of them. Initially, we have considered the variation of the average AF in the network vs. time, as reported in Fig. 1. To test the effectiveness of our algorithm, we have performed a tuning of the thresholds on the average AF δh and δl , while setting the thresholds of the single AF γh = δh and γl = δl , respectively. Recall that the average AF is a metric accounting for the lifetime decrease/increase w.r.t. to a reference scenario, i.e., all the links always powered on. If it is higher than one, then the lifetime is decreased. If it is lower than one, the lifetime is increased. In our case, the average AF tends to increase as the time under consideration increases too. This is due to two main reasons: i) the links may not be always put in SM to satisfy the traffic variations, ii) the total number of transitions tends to increase with time. However, the AF increase is governed by varying the thresholds δh and δl . Focusing on δl = 0 and δh = 1.5, we can see that the average AF is initially minimized, but, at the end of the considered period, it becomes equal to 1.15, meaning that the average link lifetime is reduced. This is due to the fact that different power state transitions have taken place, i.e., links with high AF should not be considered frequently as possible candidates to be put in SM. On the contrary, with δl = 0.6 and δh = 0.8, the AF in the first days is higher compared to the previous case, and the final AF is close to one. This is due to the fact that, initially, the algorithm tends to apply SM (resulting in an average AF lower than one). Then, as long as the threshold δh is not satisfied, AFA tends to not apply any more SM in the network, and therefore the AF tends to reach the value equal to one (i.e., all links powered on). Finally, we can see that a good tradeoff is reached by setting δl = 0.4 and δh = 0.9. Interestingly, with this setting, the final AF is equal to 0.98, meaning that the average lifetime of links is even increased compared to an always on solution. In the following, we therefore keep this setting, and we consider the variation of BS thresholds γl and γh . Fig. 2 reports the variation of γh and γl thresholds. From the figure, we can clearly see that the AF can be further controlled by properly setting these thresholds. In particular, with γl = 0.6 and γh = 0.9 the AF is higher during the initial days, while it has the lowest value at the end of the 15 period. This suggests that with this setting the algorithm is less aggressive in putting in SM links. On the contrary, when

70

1.1

60 Power Saving [%]

Average AF

1.2

1 0.9 0.8 0.7 0.6

γl=0 γh=1 γl=0 γh=1.5 γl=0.6 γh=0.8 γl=0.4 γh=0.9 γl=0.6 γh=0.9 γl=0.6 γh=1.0

MP LF AFA δl=0 δh=1.5 γl=0 γh=1.5 AFA δl=0.4 δh=0.9 γl=0.6 γh=0.8

50 40 30 20 10 0

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0

1

2

3

4

5

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Fig. 2.

AF variation vs. time: γh and γl tuning.

Fig. 4.

Number of Links in SM

80

Average AF

1.4 1.2 1 MP LF AFA δl=0 δh=1.5 γl=0 γh=1.5 AFA δl=0.4 δh=0.9 γl=0.6 γh=0.8

In the following, we consider the comparison of AFA against two energy-aware algorithms, namely LF [16] and MP [4]. Both LF and MP heuristics tend to maximize the energysavings while trying to put in SM the largest amount of links. Moreover, they always start with all links powered on for each traffic matrix. We initially compare LF, MP and AFA in terms of AF vs. time, as reported in Fig. 3. For LF and MP, we compute the AF as a postprocessing step, i.e., given the set of links in SM for each time slot. Astonishingly, both LF and MP tends to promptly increase the AF, since both of them do not consider the device lifetime during the switch off decision process. In particular, the average AF of LF and MP is equal to around 1.9 after 15 days, meaning that the lifetime of the device is reduced by a factor almost equal to 2. On the contrary, AFA is always able to limit the increase in the AF, being also able to even improve the AF w.r.t. an always on case with the most conservative parameter setting. Fig. 4. reports then the comparison of the algorithms in terms of power saving vs. time. The saving is lower during the day and higher during the night, due to the traffic variation. As expected, the largest savings are reached by one of the energyaware algorithms, namely MP. However, the AFA algorithm (with δl = 0, δh = 1.5, γl = 0, γh = 1.5) saves a comparable amount of power w.r.t. the other energy-aware algorithm (LF),

60 50 40 30 20

0 0

Time [day]

γl = 0 and γh = 1.5, the AF is lower in the first days but then is higher after 15 days. This is due to the fact that in this case AFA tends to put in SM more links, resulting also in a higher number of transitions, since these links have to be then powered on to satisfy the traffic.

70

10

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

AF variation vs. time for LF, MP and AFA.

9 10 11 12 13 14 15

MP LF AFA δl=0 δh=1.5 γl=0 γh=1.5 AFA δl=0.4 δh=0.9 γl=0.6 γh=0.8

90

1.6

Fig. 3.

8

Power Saving vs. time for LF, MP and AFA.

1.8

0.6

7

Time [day]

2

0.8

6

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15

Time [day]

Fig. 5.

Number of IP links in SM vs. time for LF, MP and AFA.

with savings topping 34% during night. Moreover, when the algorithm tends to be more conservative in terms of lifetime (with δl = 0.4, δh = 0.9, γl = 0.6, γh = 0.8), the savings are clearly lower than in the previous case. In particular, we can observe that the algorithm initially puts in SM some links during the inital days, then the set of links in SM is not changed after the fifth day in order to not impact the lifetime. Thus, we can clearly see that there exists a trade-off between energysavings and lifetime, and this trade-off is captured by the AFA thresholds. To give more insights, Fig. 5 reports the number of links in SM vs. time for the different algorithms. While both LF and MP always repeat the same trend of powered off links over the days, we can clearly see that AFA presents a different behaviour. In particular, with the most conservative setting, AFA repeats a similar day-night trend of links in SM only during the first days, and then it wisely decides to keep unchanged the set of links in SM in order to not introduce further transitions. On the other hand, with the most aggressive setting (i.e., δl = 0, δh = 1.5, γl = 0, γh = 1.5), the day-night trend is repeated over the whole set of days. However, we can clearly see that the number of links in SM during the off peak hours in decreased in the last days, suggesting that there are some links exceeding the thresholds and therefore their power state is not changed anymore. Fig. 6 then reports the AF variation over time obtained by running AFA (with δl = 0.4, δh = 0.9, γl = 0.6, γh = 0.8) for links 34-19 and 37-32 in the network. Both the links are initially put in SM, since their AF is close to the minimum one,

1

3.5

Link 34-19 Link 37-32

3 Average AF

1.1

Average AF

0.9 0.8 0.7

2.5

AFA LF MP

2 1.5 1

A

A

A

A

A

0 s =j F i

0 s =j F i

0 s =j F i

0 s =j F i

0 s =j F i

0 s =j F i

.8

.8

.8

.5

.5

.5

.2

.2

.2

.7

.5

=1 χ ij

=0 χ ij

=0 χ ij

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.5

.7

.5

.7

=1 χ ij

=0 χ ij

=0 χ ij

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0.3

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0 s =j F i

0.4

A

0 A

0.5

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0.6

0.2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 HW Parameters

Time [day]

Fig. 6.

Fig. 8.

AF variation vs. time for two IP links.

that AFA always keeps the AF close to one, therefore limiting the impact of SMs on the device lifetime.

Link 34-19 Link 37-32

ON

Power State

VI.

SM 0

1

2

3

4

5

Time [day]

Fig. 7.

HW parameters variation.

Power state transitions vs. time for two IP links.

i.e., 0.2. Then, during the first day the AF increases since both the links are powered on to satisfy the traffic increase which occurs during the day. During the second day, the AF of both links decreases again since both of them are put in SM in the night between day one and day two. However, during day two, link 37-32 is put again in SM, resulting in a decrease of the AF. Then, this link is kept in SM in the subsequent days, since its AF is lower than the γl and it is not needed any more to sustain traffic. On the other hand, link 34-19 needs to be frequently powered on to satisfy the traffic. However, the increase of its AF tends to be smoothed at the end of the observation period. To further investigate this behavior, Fig. 7 reports the variation of the power state for the two links. Interestingly, after the initial five days, link 34-19 is then always powered on (since its AF is larger than the threshold γh ), while link 37-32 is always in SM. In the last part of our work, we have performed a sensitivity analysis of the HW parameters AFijs and χij . Fig. 8 reports the comparison of AFA, LF and MP in terms of average AF at the end of the 15 days time period. From the figure, we can clearly see that both the energy-aware algorithms tend to notably increase the AF when the HW parameters are increased. In particular, when AFijs is increased the gain in putting the link in SM is reduced. Moreover, when χij is increased the penalty for passing from SM to full power (and vice-versa) is higher. These two effects are not considered by LF and MP, resulting in an AF even larger than 3, meaning that they have reduced the lifetime of the links three times compared to the one obtained with an always on solution. On the contrary, we can clearly see

C ONCLUSIONS AND F UTURE W ORK

We have investigated the problem of managing the link lifetime in a IP backbone network exploiting SMs. We have first formulated optimally the problem for the off-line case, i.e., by assuming to know the traffic over the whole time period. We have then proposed a simple heuristic, called AFA, to practically solve it for the on-line case, i.e., without requiring the knowledge of future traffic variation. AFA exploits the computation of the AF metric in order to take decisions at each time slot. We have tested AFA on a network scenario from an operator network, proving that the algorithm is able to catch the interplay between SMs and device lifetime. Moreover, AFA outperforms both the LF and the MP algorithms in terms of lifetime, while being able to save power by exploiting SMs. As next steps, we plan to perform a measurements study to better estimate the HW parameters for different types of networking equipment. Moreover, we plan to apply AFA to different types of devices in the network (routers, links, optical components), different layers (e.g., IP and optical), and different topologies. ACKNOWLEDGEMENTS The research leading to these results has received funding from the Sapienza Awards LIFETEL (University of Rome Sapienza Research Funding 2014-2015). R EFERENCES [1] M. Gupta and S. Singh, “Greening of the Internet,” in Proc. of the SIGCOMM, Karlsruhe, Germany, 2003. [2] B. Addis, A. Capone, G. Carello, L. Gianoli, and B. Sans`o, “Energy management through optimized routing and device powering for greener communication networks,” IEEE/ACM Transactions on Networling (ToN), vol. 22, pp. 313–325, Feb. 2014. [3] F. Giroire, D. Mazauric, J. Moulierac, and B. Onfroy, “Minimizing routing energy consumption: from theoretical to practical results,” in Proc. of IEEE GreenCom, Hangzhou, China, Dec. 2010. [4] L. Chiaraviglio, M. Mellia, and F. Neri, “Minimizing ISP network energy cost: Formulation and solutions,” IEEE/ACM Transactions on Networking (TON), vol. 20, pp. 463–476, Apr. 2012. [5] J. Chabarek, J. Sommers, P. Barford, C. Estan, D. Tsiang, and S. Wright, “Power awareness in network design and routing,” in Proc. of IEEE INFOCOM, Phoenix, USA, Apr. 2008. [6] P. Wiatr, P. Monti, and L. Wosinska, “Energy efficiency versus reliability performance in optical backbone networks,” Journal of Optical Communications and Networking. to appear.

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