IEEE Circuits and Systems Magazine - Q1 2023 - 65

The decoding energy consumption depends on a multitude of parameters
such as the bitrate, the frame rate, the resolution, the video codec,
and the implementation (hardware/software).
send the video stream itself. Hence, it is sufficient that
the servers manage the user accounts and the connections
between the peers.
Consequently, we model the overall yearly energy
consumption of a server based on [17] as follows
EE EE
EE
ss ss
ss
VP
,,
σσ σσ
σ
=+ +
++
,, ,, ,,VP Rx
VP copy
VP
,, ,
VP trans
,,, ,, ,,
,
(7)
,, ,
VP storeVPTxσσ+ Es
where Es,VP,σ,0 refers to a constant offset energy consumption
in idle mode, Es,VP,σ,Rx denotes the energy
consumption for receiving videos, Es,VP,σ,trans
is the energy
consumption for transcoding videos, Es,VP,σ,copy
represents the energy consumed for sending copies to
surrogate servers, Es,VP,σ,store
is the energy consumed
for storing videos, and Es,VP,σ,Tx denotes the energy consumption
for sending (transmitting) the videos to the
end users.
First, we consider the server-side energy needed to
send videos to the end users. We adopt the model proposed
in [17] that is given by
EB esr
rR
,,,, ,,
,, ,
VP Tx
σσ
σ
=⋅
∈
∑
s VP Tx
where r indicates a requested video from the set of
video requests Rs,VP,σ,Tx, which includes all requests directed
to the σ-th server. Br is the size of the requested
video in bits and es,VP,σ,send in
J
bit
is the energy consumption
needed to send a single bit to an end user. Similarly,
the energy needed to send copies of a video to surrogate
servers is given by
EBesr
rR
,,,, ,,
,, ,
VP copy
σσ
σ
=⋅
∈
∑
s VP copy
where r indicates a requested copying event of a video
from the set of copying events Rs,VP,σ,copy on the σ-th
server. For simplicity, we assume that the energy needed
to send data to an end user es,VP,σ,send from Eq. (9) is
the same as the energy needed to send data to a surrogate
server.
For receiving videos, we model the energy in a similar
manner [17], [63] such that
EB esr
rR
,,,, ,,
,, ,
VP Rx
σσ
σ
=⋅
∈
∑
s VP Rx
FIRST QUARTER 2023
s VP Rx,
(10)
ep tσσ=⋅ (12)
sr sr r ,
,, ,,,, ,,VP transdec
VP transdec
,,
IEEE CIRCUITS AND SYSTEMS MAGAZINE
65
s VP send,
(9)
s VP send,
(8)
where r indicates a request to receive a video from the
set of requests Rs,VP,σ,Rx on the σ-th server and es,VP,σ,Rx is
the energy consumption per received bit.
For the transcoding energy consumption, we take
into account that in many applications, a single input
video is transcoded to multiple videos with multiple codecs,
multiple bitrates, and with varying spatial as well
as temporal resolutions to account for differences in
user requirements and bandwidth restrictions [18]. The
corresponding energy consumption is thus split into decoding
energy consumption and encoding energy consumption
as follows:
Ee
e
s VP transVPtrans decσσ ,,
∈ s,, ,
,,,, ,,
rR VP trans
= ∑ (
+ ∑
σ
s VP
vVsr∈ VP trans
,, ,,
σ
where decoding of the video based on the r-th transcoding
request from the set of transcoding requests
Rs,VP,σ,trans
is performed once. For each transcoding request,
encoding can be performed multiple times, which
is modeled by the sum over the set of output videos
Vs,VP,σ,trans,r indexed by v. es,VP,σ,trans,r,dec is the decoding energy
consumption of the r-th video and es,VP,σ,trans,r,enc,v is
the encoding energy consumption of the v-th video for
the r-th transcoding request.
The modeling of the decoding energy consumption
was discussed in detail in [46], [47], [48], [49], [50],
and [64]. It was shown that it depends on a multitude
of video parameters such as the bitrate, the frame
rate, the resolution, the type of video codec, and the
software or hardware implementation, whichever is
used, respectively. Explicit energy consumption values
depending on these parameters can be derived
from, e.g., [47], [64]. Still, it was also shown that an
energy model solely based on the decoding time and
the mean decoding power can be sufficient for accurate
modeling [65]. We adopt this modeling approach
here to be consistent with the definition of the energy
consumption of end-user devices (see Section III-B).
Hence, the decoding energy consumption of a single
video is given by
,,σ transenc,,, ,,
rv
),
(11)
sr
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