A Survey of Internet Energy Efficiency Metrics

Kerry Hinton

1

and Fatemeh Jalali

2

1

Centre for Energy Efficient Telecommunications, University of Melbourne, Parkville, Australia

2

IBM Research, Melbourne, Australia

Keywords: Energy Consumption, Energy Efficiency, Communications Networks, Telecommunications Services,

Internet Services.

Abstract: Several metrics have been widely applied to quantify the “energy efficiency” of the Internet and ICT. In this

paper we analyse and compare these metrics when applied to telecommunication network equipment,

networks and services. We show that different metrics can imply different, and possibly conflicting,

strategies for improving energy efficiency. Some guidelines are suggested for the appropriate application of

these metrics.

1 POWER & ENERGY MODELS

1.1 Equipment Power Model

The dependence of power consumption, P(t), at time

t, on traffic throughput, C(t), for network equipment

can be written in a generic “affine” form

(Vishwanath, et al. 2014 ):

 







max idle

idle idle

max

PP

Pt P ECt P Ct

C



 

(1)

Where P

idle

is the power consumption with no

throughput (i.e. C(t) = 0), C

max

is the maximum

throughput of the network element and P

max

is the

power consumption when C(t) = C

max

. In (1) the

linear slope E = (P

max

– P

idle

)/C

max

has dimensions of

energy per bit. We shall refer to this slope as the

“incremental energy per bit”.

1.2 Network Power Model

Using (1), the total network power, P

Ntwk

, is the sum

of the equipment power;

 



,

1

E

N

Ntwk idle j j j

j

Pt P ECt







(2)

where N

E

is the number of network elements, P

idle,j

,

E

j

and C

j

(t) are the idle power, incremental energy

per bit and throughput of the j-th network element

respectively.

We have 

j

C

j

≥ C

Ntwk

, because most traffic flows

will go through multiple network elements. If we

identify all network traffic flows with a service,

including network management, control and

monitoring traffic, then we can write



1

S

N

k

Ntwk

k

Ct Ct





(3)

where N

(S)

is the number of services, k is the index

for the service and C

(k)

is the traffic (bits/sec) for the

k-th service. We also have for the traffic through the

j-th network element:



 



11

SS

NN

kkk

jj j

kk

Ct C t C t







(4)

where C

j

(k)

=



j

(k)

C

(k)

is the traffic through the j-th

network element due to service k. (



j

(k)

is the

proportion of service traffic C

(k)

that propagates

through network element j.) Note that for a service k,

we also have C

(k)

≤ 

j

C

j

(k)

.

1.3 Service Power Model

The “fundamental unit” of the Internet (as far as its

end users are concerned) is “service” (e.g. SaaS,

IaaS, Google Docs, Dropbox, etc). There has been a

growing interest in the power consumption of

services over recent years (Chan, C., et al., 2012).

From (1) we see the power consumption of a

network element has an idle power component, P

idle

,

Today, most wireline network equipment has P

idle

≥

Hinton, K. and Jalali, F.

A Survey of Internet Energy Efﬁciency Metrics.

In Proceedings of the 5th International Conference on Smart Cities and Green ICT Systems (SMARTGREENS 2016), pages 243-251

ISBN: 978-989-758-184-7

Copyright

c

243

0.8P

max

(Vishwanath, A., et al. 2014). For much of

the “Layer 0” and “Layer 1” equipment P

idle

= P

max

.

To allocate power to services, we need an approach

for allocating a proportion of P

idle

to each service

traffic flow propagating through a network element.

If







,

k

idle j

Pt

is the idle power allocated to service k in

network element j, we expect the sum over all

services through that element to satisfy



,,

1

k

idle j idle j

k

P

Pt





(5)

One way to fulfil this requirement, is to apply the

same linear proportionality rule to the idle power as

found for the incremental power in (1). That is, we

set













,

kk

idle j j

PtCt

. Using (5),







,

k

idle j

Pt

has the

form:









,,

k

kj

idle j idle j

j

Ct

PtP

Ct



(6)

With this rule, the overall power consumption of the

k-th service, P

(k)

(t) provided by the network is



,

1

E

N

idle j

kk

jj

j

P

Pt ECt

Ct













(7)

It is important to note that this is not the only

approach available. For example, we could set

















,,

ksrv

idle j idle j j

PtP N t

where N

j

(srv)

(t) is the number

of services through network element j at time t. A

disadvantage of this approach is that N

j

(srv)

(t) can be

awkwardly large for core network equipment.

2 EFFICIENCY METRICS

The ITU has described an energy-efficiency metric

in ITU-T Rec. L.1330 as (ITU-T 2012(a) ):

“The energy efficiency metric is typically defined as

the ratio between the functional unit and the energy

necessary to deliver the functional unit.”

This definition results in a metric with units

“bits/Joule”. ITU-T Rec. L.1330 also recognises that

“The inverse metric, energy divided by functional

unit, could be used as an alternative.”

We shall focus on “energy per bit” metrics.

2.1 Standardised Metrics

Energy efficiency metrics currently used in

standards documents are based on the ratio of power

to traffic for a number, M, of pre-defined load levels

of the equipment (Minoli, D., 2011). For example,

the ECR-VL is defined by the ratio,



 

11

MM

mm m m

mm

ECR a P a C



 



(8)

Where ∑

m

a

m

= 1, P

m

and C

m

are the power and the

pre-defined loads indexed by m. The values of P

m

and C

m

are specified in the definition and depend

upon the type of network element.

For a network element, placing (1) into (8) gives

idle

max m m

m

P

ECR E

Cab







(9)

Where b

m

= C

m

/C

max

. Example values for b

m

are: b

1

=

1, b

2

= 0.5, b

3

= 0.3, b

4

= 0.1 and b

5

= 0 with

corresponding weights a

1

= 0.1, a

2

= 0.5, a

3

= 0.3, a

4

= 0 and a

5

= 0.1 (Minoli, D., 2011).

There are several problems with this and similar

metrics (TEER, EER and TEEER) (Minoli, D.,

2011). First, although these definitions include

averages over loads, they effectively correspond to a

single load; therefore the value does not incorporate

the impact of traffic variation over the diurnal cycle.

Another is seen by considering two routers with

the (approximately) same C

max

but different values

for P

idle

and E. Let the values for the routers be

P

idle,1

, E

1

and P

idle,2

E

2

respectively and P

idle,2

=

xP

idle,1

where x is constant. Then we get the same

ECR value for both routers provided:



,1

21

1

idle

max m m

m

P

EE x

Cab







(10)

If we set x = 0 router 2 is load proportional (i.e.

P

idle,2

= 0) which is viewed as desirably energy

efficient. However it still has the same ECR as

router 1 which may have large idle power.

Using the value for x given by

1

,1

1

max

mm

m

idle

EC

x

ab

P











(11)

in (10) gives E

2

= 0 which is often considered

energy inefficient but will still have the same ECR

as router 1. Hence ECR type metrics do not reflect

the idea of “energy efficiency” very well.

Finally, the metric defined in (8) does not lend

itself to being applied to networks or services. It is

not clear how to apply this metric to a collection of

interconnected network elements. Even less apparent

is how to apply this metric to service that may be

one of many propagating through an element.

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244

2.2 Defining Energy Efficiency

In this work we will study a range of metrics that

have been proposed and applied (Schien, D, and

Preist, C. 2014)(GreenTouch, 2015)(Baliga, J., et al.

2009). We will implement them in a manner that is

applicable to network elements, networks and

services. Simple energy/bit efficiency metrics that

have been employed in the literature are:

a) “Instantaneous energy per bit” defined by the

ratio of the instantaneous power to throughput:



1

Pt

Ht

Ct



(12)

This metric has been adopted in a range of “bottom-

up” metrics used to calculate the energy efficiency

of the Internet at peak load (Baliga, J., et al. 2009) or

at time t (Chiaraviglio, L., et al., 2009). When

P

idle

≠ 0,

1

H(t) will vary over the diurnal cycle.

b) “Energy per bit” defined by the ratio of total

energy, E(T), consumed over duration T to total bit

throughput. B(T), over duration T:



2

0

()

T

Ptdt

P

T

HT

TC

Ctdt





E

B

(13)

In this equation the time integral is over duration T

from a pre-determined origin time. The GreenTouch

consortium uses 1/(

2

H(T)) with T = 1 year for the

years 2010 and 2020 (GreenTouch, 2015). In (13)

X

T

= 

T

X(t)dt/T.

Some “top-down” metrics use (13), with E(T)

determined from information such as equipment

deployment inventory data and energy consumption

and B(T) is an assessment of the total network traffic

(Schien, D, and Preist, C. 2014).

c) “Mean instantaneous energy per bit” was

proposed in (ITU-T 2012(b)), although that

document contains a mathematical error. The

average the instantaneous metric over time duration

T is defined by:



31

0

1

T

Pt

P

HT dt Ht

TCt C





(14)

Other metrics have been defined, for example

mobile network researchers have used power per

unit area (Tombaz, S. et al. 2013). Due to lack of

space, in this work we will focus on the energy per

bit metrics,

1

H,

2

H and

3

H, listed above.

2.3 Uses of Metrics

Metrics are most frequently used for improvement

(i.e developing strategies to change the value of the

metric for a system), benchmarking (comparing the

value of a metric for the systems being

benchmarked) or estimating energy consumption.

When used for improvement, the choice of metric

will directly impact the strategies adopted for

“improvement”. When used for benchmarking, the

choice of metric will determine what we mean when

we say one system is “better” than another.

Therefore, the choice of metric is important.

3 DIURNAL CYCLES

Diurnal traffic cycles result from the fact that many

users are typically “off-line” and “on-line” during

common times over a 24 hour period. An example of

a diurnal cycle for an Australian city (taken from an

edge router traffic log) is shown by the solid line in

Fig. 1. Also shown is a pure sinusoidal

approximation (dashed line) of the 24 hour diurnal

cycle. In general, traffic diurnal cycles can

dramatically vary in shape; however they all have a

cyclic profile.

For the purposes of comparing the general

characteristics of these metrics we shall use a “first-

order” sinusoidal approximation for the diurnal

cycle of the k-th service’s traffic flow (in bits/sec) of

the form



  



cos 2

kkk k

mean

CtC C tT



 

(15)

with T = 24 hours. In (15)



k

mean

C

is the mean traffic

for the k-th service flow over duration T and C

(k)

the variation away from the mean for the k-th flow.

The phase



(k)

accounts for the fact that the diurnal

cycles of the individual services may not be

synchronized (i.e. different services will have a

different time of peak traffic). Using (15) enables the

calculation of closed forms for the metrics above.

Figure 1: Example of a 7 day diurnal cycle from a

commercially deployed router (solid line) and a first-order

sinusoidal approximation (dashed line).

A Survey of Internet Energy Efﬁciency Metrics

245

The form in (15) can be applied to equipment

and networks. From (3) the time dependence of the

total network traffic is the sum of all the service

traffics:













 



1

cos 2

S

Ntwk mean,Ntwk Ntwk Ntwk

N

kk k

mean

k

CtC C tT

CC tT





 



(16)

Similarly, from (4) the total traffic for the j-th

network element, C

j

(t), will have the form:













 



  



1

cos 2

S

jmean,jj j

N

kk k

mean, j j

k

N

kk k k

jmean

k

Ct C C tT

CC tT







 



(17)

The



terms correspond to the location of the peak

load within the diurnal cycle relative to a fixed

arbitrary origin. Setting the time origin to time t

0

(hours) then if the peak traffic occurs at time t

peak

,

we have



= 2



(t

peak

– t

0

)/24.

For a network or element in which the flows are

synchronized (i.e. all flows have the same peak

traffic time) we have



,,

11

,,,,

11

SS

NN

kk

mean Ntwk mean max Ntwk max

kk

NN

kk

mean j mean j max j max j

kk

CCCC





(18)

However, with unsynchronized flows, we get



   







1

1/ 2

2

1

cos

cos 2

S

SSS

N

k

Ntwk mean

k

NNN

kklkl

kkll

Ntwk

Ct C

CCC

tT















  













(19)

where

 



 

1

11

tan sin cos

S

N

kk k k

Ntwk

kk

CC









  







(20)

A corresponding form can be written for C

j

(t).

Assuming the differences (



(k)

–



(l)

) is are not all

zero, then comparing a network with many

synchronized flows to the same network with many

unsynchronized flows we find,

,,

Ntwk Ntwk

mean Ntwk mean Ntwk

s

ynch unsynch

CC





(21)

Taking this further, if the phases,



(k)

, are

uniformly, randomly distributed



 

1/ 2

2

,

k

Ntwk

Sk

mean Ntwk

unsynch

mean

C

NC





(22)

From this we see that as the number of

unsynchronised flows increases the network traffic

maximum, given by C

mean,Ntwk

+ C

Ntwk

, reduces to

the mean, C

mean,Ntwk

;



max,

,,

,

lim

lim 1

S

Ntwk

N

Ntwk

mean Ntwk mean Ntwk

N

mean Ntwk

C

CC

C

















(23)

This means the depth of the diurnal cycle reduces

when increasingly many unsynchronised traffic

flows are brought together. This result applies to any

single network element, network facility or overall

network that deals with many service flows.

The results in (21) (22) and (23) tell us that

facilities dealing with highly synchronised traffic

(such as serving only a local time-zone) are likely to

experience a relatively deeper diurnal cycle than

those dealing with unsynchronised traffic (such as

traffic from geographically diverse regions around

the globe).

Diurnal cycle depth plays an important role when

improving energy efficiency, because networks are

dimensioned to accommodate peak traffic (C

max

). In

legacy networks equipment remains fully energised

24/7, therefore dimensioning network for peak load

means that during off-peak hours equipment is lowly

utilised which is less energy inefficient (i.e. higher

energy per bit) than at peak time.

In new generation networks, a widely proposed

strategy is to implement low energy (sleep) states

during “off-peak” times to improve energy

efficiency (Mahadevan, P. et al., 2009). The depth of

the diurnal cycle is important because it indicates

how much equipment can be powered-down during

off peak times (GreenTouch, 2015).

4 THE METRICS

4.1 Network Equipment

Without a loss of generality, we can drop the phase

term when applying the diurnal cycle to the traffic

through a network element. For the j-th network

element, we have

SMARTGREENS 2016 - 5th International Conference on Smart Cities and Green ICT Systems

246



,

1

,

2

,

3

1/2 1/2

,,

cos 2

idle j

jj

mean j j

idle j

jj

mean j

idle j

jj

min j max j

P

Ht E

CC tT

P

HT E

C

P

HT E

CC









(24)

where C

min,j

= C

mean,j

- C

j

. To calculate

3

H

j

(T) we

have used Item 3.613.1 from (Gradshteyn, I. Ryzhik,

I. 1980).

We note that C

mean

= C

T

, therefore we could

interpret the difference between

2

H(T) and

3

H(T)

results from the former using the arithmetic mean of

the traffic C(t) whereas the latter uses the geometric

mean (for sinusoidal traffic load).

Figure 2: Plot of the ratio

3

H(T)/

2

H(T) showing that the

metric

3

H(T) reflects the impact of durations of low

utilisation on network energy/bit metric for equipment in

which idle power dominates.

Comparing

2

H

j

(T) and

3

H

j

(T) in (24) we note that

3

H

j

(T) reflects the impact of traffic variation over a

diurnal cycle where-as

2

H

j

(T) does not. We see this

by calculating the ratio

3

H

j

(T)/

2

H

j

(T) over a range

diurnal cycle depths (C

min

/C

max

) for the network

element traffic as shown in Fig. 2.

2

H

j

(T) is constant

with respect to the ratio (C

min

/C

max

) where-as

3

H

j

(T)

exposes the impact of periods of low utilisation

which correspond to low values of (C

min

/C

max

).

4.2 Networks

For a network using (2) and (3) we have



,

1

,

2

cos

cos 2

E

N

idle j j mean, j j j

j

Ntwk

mean Ntwk Ntwk

t

PEC C

T

Ht

CC tT











 











(25)



,

1

2

,,

E

N

idle j j mean, j

Eidle mean

j

EE E

Ntwk

mean Ntwk mean Ntwk

PEC

NP EC

HT

CC









(26)



3

,

1/2 1/ 2

1

,,

1/2 1/ 2

,,

1/2 1/ 2

,,

1

1cos

E

N

Ntwk idle j

j

min Ntwk max Ntwk

max Ntwk min Ntwk

j

jmean,j j

mean, j

max Ntwk min Ntwk

HT P

CC

C

EC

C

CC







































(27)

The notation X

E

represents an average over

network elements, defined by

1

E

N

j

E

j

E

XX

N





(28)

The approximations in (26) and (27)is justified by

the fact that E

j

and C

j

are independent random

variables hence EC

E

 E

E

C

E

.

In

3

H

Ntwk

(T),



j

is measured relative to the

network peak traffic time, that is



j

= 2



(t

peak,j

–

t

peak,Ntwk

)/24. To calculate (27) we have used Items

2.554.2 and 2.553.2 from (Gradshteyn, I. Ryzhik, I.

1980).

From (27) the factors that feed into

3

H

Ntwk

(T) are

the relative depths of the traffic diurnal cycles,

C/C

mean

, and the degree of synchronisation of the

traffic flows,



(k)

(see (17)). To acquire an

appreciation of the impact of these parameters on the

metrics, a mesh network simulation was constructed.

The simulated network consisted of 50 inter-

connected network elements (N

E

= 50) each with a

power profile given by (1) with a range of values for

P

idle

(randomly selected in the range 1kW to 1.5kW)

and E (randomly selected in the range 0.5 nJ/bit to 2

nJ/bit). These values are typical of current

generation router and switch technology (Van

Heggegham, W., et al., 2012). The network carries

500 sinusoidal service flows (N

(S)

= 500), with mean

flow data rates randomly distributed over the range

0.5 Gbit/s ≤ C

mean

≤ 2 Gbit/s. Each flow travels

through 10 network elements randomly selected

from the 50 elements in the simulation. No flow

travels through the same element more than once.

Although the simulation is a mesh network, the

architecture is not a major influence because the

overall power consumption is determined by the

equipment along the service flow paths not the

global network architecture.

The synchronisation of the flows is parametrised

by quantity b with the phase of the flows chosen

randomly over the range -b



≤



(k)

≤ b



. For highly

synchronised flows we set b = 0.1. For totally

desynchronised flows we set b = 1. The simulation is

run for values of b from 0.1to 1.0 in steps of 0.1.

To parametrise the diurnal cycle depth, C/C

mean

the flows are distributed randomly over a range

C/C

mean

to C/C

mean

+ 0.2 with values of C/C

mean

A Survey of Internet Energy Efﬁciency Metrics

247

from 0.1 to 0.8 in steps of 0.1.

For the case of synchronised flows and a deep

diurnal cycle in the simulated network, the value of

1

H

Ntwk

(t) can vary dramatically over the diurnal

cycle. For the simulated network described above, at

peak traffic time, we get

1

H

Ntwk

(t

peak

)  66 nJ/bit. At

the time of minimum traffic (t

trough

)

1

H

Ntwk

(t

trough

) 

910 nJ/bit. Therefore using this metric requires

careful consideration of the time at which it is

measured. Measuring at peak traffic time will give a

low estimate for typical energy per bit. From (25)

and (26), for a totally desynchronised network we

have

1

H

Ntwk

(t) 

2

H

Ntwk

(T) for all t over the diurnal

cycle. For the simulated network, this situation gives

1

H

Ntwk

(t) 

2

H

Ntkw

(T)  113 nJ/bit.

The values of

2

H

Ntwk

(T) and

3

H

Ntwk

(T) (T = 24

hours) for ranges of cycle depth, C/C

mean

, and

synchronisation, b, are shown by the surface plot in

Fig. 3. The top left region of the surface plots

corresponds to highly synchronised service traffic

flows with relatively deep diurnal cycles. We see

that

3

H

Ntwk

(T) reflects the impact of periods of low

network utilisation that occur in networks with

highly synchronised traffic and a deep diurnal cycle.

In contrast

2

H

Ntwk

(T) 

3

H

Ntwk

(T) for networks that

are desynchronised or have shallow diurnal cycles.

Figure 3: Surface plots of

2

H

Ntwk

(T) and

3

H

Ntwk

(T) for

values of synchronicity parameter b and diurnal cycle

depth C/C

mean

.

4.3 Services

Using the equations above, for the k-th service

 



,

11

()

EE

NN

k k idle j k

jjjj

jj

j

P

Ht E Ht

Ct















(29)



2

1/ 2 1/ 2

,,

,

1/ 2 1/2

1/ 2 1/ 2

1

,,

1

1cos

E

k

N

max j min j

jidlej k

j

k

j

min j max j

max j min j

mean

N

k

jj

j

HT

CC

P

C

CC

C

E































(30)



 



,

3 3

1/2 1/ 2

11

,,

EE

NN

kkidlej k

jjjj

jj

min j max j

P

HT E HT

CC















(31)

In (30)



j

(k)

is the offset between the peak traffic time

of the j-th network and the peak traffic time of the k-

th service.

If all the services in the network are similarly

synchronised (i.e. no service is significantly out of

synch with all the other services) we get for all k;



,

2

1

,

E

k

N

k j idle j k

jj

j

mean j

P

HT E

C









(32)

To graphically display the dependence of

2

H

(k)

(T)

and

3

H

(k)

(T) on the parameters C/C

mean

and b, we

average over the k-index; i.e. over the services

giving;



1

S

N

S

kkS

XX

k

HT HTN





(33)

where X is 2 or 3.

Plotting the simulation results for 

2

H

(k)

(T)

(S)

and



3

H

(k)

(T)

(S)

, we get identical surface plots as in fig.

3. That is, for the simulation scenario

2

H

Ntwk

(T) =



2

H

(k)

(T)

(S)

and

3

H

Ntwk

(T) = 

3

H

(k)

(T)

(S)

. This can be

shown to hold in general provided all of C

mean,j

fall

within a limited range of values.

It is important to note that

X

H

(k)

(T) 

X

H

Ntwk

(T)

only applies when all the services are all similarly

synchronised such that the phase,



(k)

, of each

service is within a given range (parametrised by b)

of all other services.

For a service that is significantly out of

synchronisation with the other services, the value of

2

H

(k)

(T) is significantly greater. For example,

consider a service k for which



(k)

well away from

zero and



(l)

 0 for all l ≠ k. In this case the network

is highly synchronised with only flow k well out of

synch. In this situation, C

max,j

>> C

min,j

for all j.

Using (30) we get



 



 

2

,

1/2 1/2

11

,,

,

1/2 1/2

11

,,

1

2

EE

k

NN

jidlej k k

jj

k

jj

min j max j

mean

k

NN

jidlej k k

jj

min j max j

HT

P

C

E

CC

C

P

E

CC















 





 



(34)

SMARTGREENS 2016 - 5th International Conference on Smart Cities and Green ICT Systems

248

Fig. 4 is a surface plot of

2

H

(k)

(T) for a service

with



(k)

=



for all values of b. We see that an out-

of-synch service has much higher energy per bit than

the other, (in-synch) services when the network is

highly synchronised. As the degree of

synchronisation reduces or the diurnal cycle depth

reduces,

2

H

(k)

(T) reduces to that of the other services.

Figure 4: Surface plot for

2

H

(k)

(T) for a service (



) out of

phase with all other services in the network. Low values of

b correspond to all other flows across the network being

highly synchronised.

Comparing Fig. 3(a) and Fig. 4, we see that service

operators wishing to minimise the energy per bit of

their service will want to avoid being significantly

out-of-synch with the majority of services. This will

lead to service providers trying to synchronise their

services with everyone else. This, in turn, will lead

to deeper diurnal cycles and the resulting over-

dimensioning of the network, mentioned in Section

4, and consequential increase in energy

consumption.

5 APPLICATIONS

The expressions for the H metrics above are all

based on a pure sinusoidal diurnal cycle. In real

networks the diurnal cycle is not a pure sinusoid.

However, generalising these metrics to arbitrary

diurnal cycle profiles is relatively simple. For

1

H(t),

we just replace the sinusoid with the actual diurnal

cycle from collected traffic data. Because

2

H

j

(T) and

2

H

Ntwk

(T) only involve C

mean

, these are directly

applicable to any diurnal cycle profile.

The

2

H

(k)

(t) and

3

H metrics involve quantities

C

max

, C

min

, C and



. To generalise these metrics we

replace these values, in the metric definitions, with

their means over multiple diurnal cycles: C

max



D

,

C

min



D

, C

D

and 





D

which can be extracted from

traffic data collected over multiple days. Where a

quantity is raised to a power, a, we replace X

a

by

(X

D

)

a

. Our discussion from now on can be applied

to these generalised forms.

As discussed above, metrics

1

H(t) and

2

H(T) are

already widely used where-as the

3

H(T) metric is

not. The advantage provided by the

3

H(T) metric is

that it quantifies the impact of the shape of the

diurnal cycle and its relationship to other traffic

flows (via C

max

, C

min

and



). This enables us to

quantify the impact of changing traffic profiles on

energy efficiency of networks and services.

Although the energy efficiency metrics have

primarily been created to provide a quantitative

measure of “energy efficiency” (ITU-T 2012 (a))(

Coroama, V. Hilty, L. 2014), they have been also

used to estimate the power consumption of

equipment, networks and services (Baliga, J., et al.

2009)(Van Heggegham, W., et al.,

2012)(Vishwanath, A., et al. 2015). We will now

consider some issues with these applications

5.1 Deployed Networks

The application of the metrics above in real

networks can be very problematic due to

unavailability of or difficulty in attainting the

required data. In particular, evaluating these metrics

for a network or service may require collection of a

significant amount of data not readily available.

Therefore approximations for the metrics can make

evaluation easier, although possibly at the cost of

reduced accuracy. Also, the inter-relationships

between the metrics may allow the data collected for

one metric to be used to evaluate another.

Using (26) we can show that



2

1

idle

Ntwk hops E

E

P

HN E

C





 







(35)

where N

hops

 is the mean number of hops for service

traffic across the network. This form aligns with the

expressions for edge and core network energy

efficiency in (Baliga, J., et al. 2009)(Van

Heggegham, W., et al., 2012).

As discussed above, the simulation results show

the

2

H metric for a network is approximately equal

to the mean

2

H metric across the services, that is:

2

H

Ntwk

(T)  

2

H

(k)

(T)

(S)

. The results also show the

variance 

(S)

of the services satisfies



(S)

(

X

H

(k)

(T)) < 0.1 

X

H

(k)

(T)

(S)

. This means that, to a

first order approximation, provided all the services

in the network are roughly synchronised to the same

degree (i.e. no services are significantly out of

synchronisation with the other services), we have



 

22

k

Ntwk

HT H T

(36)

A Survey of Internet Energy Efﬁciency Metrics

249

for most of the services transported by the network.