Online Algorithms for Geographical Load Balancing
Minghong Lin
∗
, Zhenhua Liu
∗
, Adam Wierman
∗
, Lachlan L. H. Andrew
†
∗
California Institute of Technology, Email: {mhlin,zhenhua,adamw}@caltech.edu
†
Swinburne University of Technology, Email: landrew@swin.edu.au
Abstract—It has recently been proposed that Internet energy
costs, both monetary and environmental, can be reduced by
exploiting temporal variations and shifting processing to data
centers located in regions where energy currently has low cost.
Lightly loaded data centers can then turn off surplus servers.
This paper studies online algorithms for determining the number
of servers to leave on in each data center, and then uses these
algorithms to study the environmental potential of geographical
load balancing (GLB). A commonly suggested algorithm for this
setting is “receding horizon control” (RHC), which computes the
provisioning for the current time by optimizing over a window
of predicted future loads. We show that RHC performs well
in a homogeneous setting, in which all servers can serve all
jobs equally well; however, we also prove that differences in
propagation delays, servers, and electricity prices can cause RHC
perform badly, So, we introduce variants of RHC that are guar-
anteed to perform as well in the face of such heterogeneity. These
algorithms are then used to study the feasibility of powering a
continent-wide set of data centers mostly by renewable sources,
and to understand what portfolio of renewable energy is most
effective.
I. INTRODUCTION
Energy consumption of data centers is a major concern
to both operators and society. Electricity for Internet-scale
systems costs millions of dollars per month [1] and, though
ICT uses only a small percentage of electricity today, the
growth of electricity in ICT exceeds nearly all sectors of the
economy. For these reasons, and more, ICT must play its part
in reducing our dependence on fossil fuels.
This can be achieved by using renewable energy to power
data centers. Already, data centers are starting to be powered
by a greener portfolio of energy [2], [3], [4]. However, achiev-
ing a goal of powering data centers entirely with renewable
energy is a significant challenge due to the intermittency and
unpredictability of renewable energy. Most studies of powering
data centers entirely with renewable energy have focused on
powering individual data centers, e.g., [5], [6]. These have
shown that it is challenging to power a data center using only
local wind and solar energy without large-scale storage, due
to the intermittency and unpredictability of these sources.
The goal of this paper is twofold: (i) to illustrate that the ge-
ographical diversity of Internet-scale services can significantly
improve the efficiency of the usage of renewable energy, and
(ii) to develop online algorithms that can realize this potential.
Many papers have illustrated the potential for using “ge-
ographical load balancing” (GLB) to exploit the diversity of
Internet-scale service and provide significant cost savings for
data centers; see [1],[7]–[9]. The goal of the current paper is
different. It is to explore the environmental impact of GLB
within Internet-scale systems. In particular, using GLB to re-
duce cost can actually increase total energy usage: reducing the
average price of energy shifts the economic balance away from
energy saving measures. However, more positively, if data
centers have local renewable energy available, GLB provides
a huge opportunity by allowing for “follow the renewables”
routing.
Research is only beginning to quantify the benefits of
this approach, e.g., [10] and [11]. Many questions remain.
For example: Does “follow the renewables” routing make it
possible to attain “net-zero” Internet-scale services? What is
the optimal mix of renewable energy sources (e.g. wind and
solar) for an Internet-scale service? To address these questions,
we perform a numerical study using real-world traces for
workloads, electricity prices, renewable availability, data center
locations, etc. Surprisingly, our study shows that wind energy
is significantly more valuable than solar energy for “follow
the renewables” routing. Commonly, solar is assumed to be
more valuable given the match between the peak traffic period
and the peak period for solar energy. Wind energy lacks this
correlation, but also has little correlation across locations and
is available during both night and day; thus the aggregate wind
energy over many locations exhibits much less variation than
that of solar energy [12].
Our numerical results suggest that using GLB for “follow
the renewables” routing can provide significant environmental
benefits. However, achieving this is a challenging algorithmic
task. The benefits come from dynamically adjusting the routing
and service capacity at each location, but the latter incurs
a significant “switching cost” in the form of latency, energy
consumption, and/or wear-and-tear. Further, predictions of the
future workload, renewable availability, and electricity price
are inaccurate beyond the short term. Thus online algorithms
are required for GLB.
Although the distant future cannot be known, it is often
possible to estimate loads a little in the future [13]. These
predictions can be used by algorithms such as Receding Hori-
zon Control (RHC), also known as Model Predictive Control,
to perform geographical load balancing. RHC is commonly
proposed to control data centers [14], [15] and has a long
history in control theory [16]. In RHC, an estimate of the near
future is used to design a tentative control trajectory; only the
first step of this trajectory is implemented and, in the next time
step, the process repeats.
Due to its use in systems today, we begin in Section III
by analyzing the performance of RHC applied to the model
of Section II. In particular, we study its competitive ratio: the
worst case ratio of the cost of using RHC to the cost of using
optimal provisioning based on perfect future knowledge. We
prove that RHC does work well in some settings, e.g., in
a homogeneous setting (where all servers are equally able
to serve every request) RHC is 1 + O(1/w)-competitive.
This can be much tighter than the competitive ratio of 3
obtained by schemes unaware of future loads [17]. However, in
general, RHC can perform badly for the heterogeneous settings
needed for geographical load balancing. In general, RHC is
1 + Ω(β/e
0
)-competitive, where β measures the switching
cost and e
0
is the cost of running an idle server. This can
be large and, surprisingly, does not depend on w. That is, the
worst case bound on RHC does not improve as the prediction
window grows.
Motivated by the weakness of RHC in the general context
of geographical load balancing, we design a new algorithm in
Section III called Averaging Fixed Horizon Control (AFHC).
AFHC works by taking the average of w + 1 Fixed Hori-
zon Control (FHC) algorithms. Alone, each FHC algorithm
seems much worse than RHC, but by combining them AFHC
achieves a competitive ratio of 1 + O(1/w), superior to that
of RHC. We evaluate these algorithms in Section IV under
real data center workloads, and show that the improvement in
worst-case performance comes at no cost to the average-case
performance.
Note that the analysis of RHC and AFHC applies to a very
general model. It allows heterogeneity among both the jobs
and the servers, whereas systems studied analytically typically
have homogeneous servers [17]–[19] or disjoint collections
thereof [20].
II. MODEL
Our focus is on understanding how to dynamically pro-
vision the (active) service capacity in geographically diverse
data centers serving requests from different regions so as to
minimize the “cost” of the system, which may include both
energy and quality of service. In this section, we introduce
a simple but general model for this setting. Note that the
model generalizes most recent analytic studies of both dynamic
resizing within a local data center and geographical load
balancing among geographically distributed data centers, e.g.,
including [10],[21],[17],[1].
A. The workload
We consider a discrete-time model whose timeslot matches
the timescale at which routing decisions and capacity provi-
sioning decisions can be updated. There is a (possibly long)
interval of interest t ∈ {1, . . . , T }. There are J geographically
concentrated sources of requests, and the mean arrival rate at
time t is denoted by λ
t
= (λ
t,j
)
j∈{1,...,J }
, where λ
t,j
is the
mean request rate from source j at time t. We set λ
t
= 0
for t < 1 and t > T . In a real system, T could be a year, a
timeslot could be 10 minutes.
B. The Internet-scale system
We model an Internet-scale system as a collection of S
geographically diverse data centers, where data center s ∈ S
is modeled as a collection of M
s
homogeneous servers.
1
We
seek the values of two key GLB parameters:
(i) λ
t,j,s
, the amount of traffic routed from source j to data
center s at time t, such that
P
S
s=1
λ
t,j,s
= λ
t,j
.
(ii) x
t
= (x
t,s
)
s∈{1,...,S}
, where x
t,s
∈ {0 , . . . , M
s
} is the
number of active servers at data center s at time t.
The objective is to choose λ
t,j,s
and x
t
to minimize the “cost”
of the system, which can be decomposed into two components:
(i) The operating cost incurred by using active servers. It
includes both the delay cost (revenue loss) which depends
on the dispatching rule through network delays and the
1
Note that a heterogeneous data center can simply be viewed as multiple
data centers, each having homogeneous servers.
load at each data center, and also the energy cost of the
active servers at each data center with particular load.
(ii) The switching cost incurred by toggling servers into and
out of a power-saving mode between timeslots (including
the delay, migration, and wear-and-tear costs).
We describe each of these in detail below.
1) Operating cost: The operating cost is the sum of the
delay cost and the energy cost. Each is described below.
Delay cost: The delay cost captures the lost revenue
incurred because of the delay experienced by the requests. To
model this, we define r
t
(d) as the lost revenue associated with
a job experiencing delay d at time t, which is an increasing and
convex function. The delay has two components: the network
delay experienced while the request is outside of the data
center and the queueing delay experienced while the request
is at the data center.
We model the network delays by a fixed delay δ
t,j,s
expe-
rienced by a request from source j to data center s during
timeslot t. We make no requirements on the structure of the
δ
t,j,s
. We assume that these delays are known within the
prediction window w.
To model the queueing delay, we let q
s
(x
t,s
,
P
j
λ
t,j,s
)
denote the queueing delay at data center s given x
t,s
active
servers and an arrival rate of
P
j
λ
t,j,s
. Further, for stability,
we must have that
P
j
λ
t,j,s
< x
t,s
µ
s
, where µ
s
is the
service rate of a server at data center s. Thus, we define
q
s
(x
t,s
,
P
j
λ
t,j,s
) = ∞ for
P
j
λ
t,j,s
≥ x
t,s
µ
s
.
Combining the above gives the following model for the total
delay cost D
t,s
at data center s during timeslot t:
D
t,s
=
J
X
j=1
λ
t,j,s
r
t
q
s
x
t,s
,
X
j
′
λ
t,j
′
,s
+ δ
t,j,s
. (1)
We assume that D
t,s
is jointly convex in x
t,s
and λ
t,j,s
. Note
that this assumption is satisfied by most standard queueing
formulae, e.g., the mean delay under M/GI/1 Processor Sharing
(PS) queue and the 95th percentile of delay under the M/M/1.
Energy cost: To capture the geographic diversity and vari-
ation over time of energy costs, we let f
t,s
(x
t,s
,
P
j
λ
t,j,s
)
denote the energy cost for data center s during timeslot t
given x
t,s
active servers and arrival rate
P
j
λ
t,j,s
. For every
fixed t, we assume that f
t,s
(x
t,s
,
P
j
λ
t,j,s
) is jointly convex in
x
t,s
and λ
t,j,s
. This formulation is quite general, and captures,
for example, the common charging plan of a fixed price per
kWh plus an additional “demand charge” for the peak of the
average power used over a sliding 15 minute window [22].
Additionally, it can capture a wide range of models for server
power consumption, e.g., energy costs as an affine function of
the load, see [23], or as a polynomial function of the speed,
see [24], [25]. One important property of f
t,s
for our results
is e
0,s
, the minimum cost per timeslot for an active server of
type s. i.e., f
t,s
(x
t,s
, ·) ≥ e
0,s
x
t,s
.
The total energy cost of data center s during timeslot t is
E
t,s
= f
t,s
x
t,s
,
X
j
λ
t,j,s
. (2)
2) Switching cost: For the switching cost, let β
s
be the cost
to transition a server from the sleep state to the active state at
data center s. We assume that the cost of transitioning from
the active to the sleep state is 0. If this is not the case, we can
simply fold the corresponding cost into the cost β
s
incurred
in the next power-up operation. Thus the switching cost for
changing the number of active servers from x
t−1,s
to x
t,s
is
d(x
t−1,s
, x
t,s
) = β
s
(x
t,s
− x
t−1,s
)
+
,
where (x)
+
= max(0, x). The constant β
s
includes the costs
of (i) the energy used toggling a server, (ii) the delay in
migrating state, such as data or a virtual machine (VM), when
toggling a server, (iii) increased wear-and-tear on the servers
toggling, and (iv) the risk associated with server toggling. If
only (i) and (ii) matter, then β
s
is either on the order of the
cost to run a server for a few seconds (waking from suspend-
to-RAM or migrating network state [26] or storage state [27]),
or several minutes (to migrate a large VM [28]). However, if
(iii) is included, then β
s
becomes on the order of the cost to
run a server for an hour [29]. Finally, if (iv) is considered then
our conversations with operators suggest that their perceived
risk that servers will not turn on properly when toggled is high,
so β
s
may be even larger.
C. Cost optimization problem
Given the workload and cost models above, we model the
Internet-scale system as a cost-minimizer. In particular, we
formalize the goal of the Internet-scale system as choosing
the routing policy λ
t,j,s
and the number of active servers x
t,s
at each time t so as to minimize the total cost during [1 , T ].
This can be written as follows:
min
x
t,s
,λ
t,j,s
T
X
t=1
S
X
s=1
E
t,s
+ D
t,s
+ d(x
t−1,s
, x
t,s
) (3)
s.t.
X
S
s=1
λ
t,j,s
= λ
t,j
, ∀t, ∀j
λ
t,j,s
≥ 0, ∀t, ∀j, ∀s
0 = x
0,s
≤ x
t,s
≤ M
s
, ∀t, ∀s
The above optimization problem is jointly convex in λ
t,j,s
and x
t,s
, thus in many cases the solution can be found easily
offline, i.e., given all the information in [1, T ]. However, our
goal is to find online algorithms for this optimization, i.e.,
algorithms that determine λ
t,j,s
and x
t,s
using only informa-
tion up to time t + w where w ≥ 0 is called the “prediction
window”. Based on the structure of optimization (3), we can
see that λ
t,j,s
can be solved easily at timeslot t once x
t,s
are
fixed. Thus the challenge for the online algorithms is to decide
x
t,s
online.
D. Generalizations
Although the optimization problem (3) is very general
already, the online algorithms and results in this paper ad-
ditionally apply to the following, more general framework:
min
x
1
,...,x
T
T
X
t=1
h
t
(x
t
) +
T
X
t=1
d(x
t−1
, x
t
) (4)
subject to 0 ≤ x
t
∈ R
S
, x
0
= 0.
where x
t
has a vector value and {h
t
(·)} are convex functions.
Importantly, this formulation can easily include various SLA
constraints on mean queueing delay or the queueing delay
violation probability. In fact, a variety of additional bounds on
x
t
can be incorporated implicitly into the functions h
t
(·) by
extended-value extension, i.e., defining h
t
(·) to be ∞ outside
its domain.
To see how the optimization problem (3) fits into this general
framework, we just need to define h
t
(x
t
) for feasible x
t
as the
optimal value to the following optimization over λ
t,j,s
given
x
t,s
fixed:
min
λ
t,j,s
X
S
s=1
(E
t,s
+ D
t,s
) (5)
s.t.
X
S
s=1
λ
t,j,s
= λ
t,j
, ∀j
λ
t,j,s
≥ 0 , ∀j, ∀s
For infeasible x
t
(x
t,s
6∈ [0, M
s
] for some s) we define
h
t
(x
t
) = ∞. We can see that the optimal workload dispatching
has been captured by the definition of h
t
(x
t
). Note that other
restrictions of workload dispatching may be incorporated by
the definition of h
t
(x
t
) similarly.
Intuitively, this general model seeks to minimize the sum of
a sequence of convex functions when “smooth” solutions are
preferred, i.e., it is an online smooth convex optimization prob-
lem. This class of problems has many important applications,
including more general capacity provisioning in geographically
distributed data centers, video streaming [30] in which en-
coding quality varies but large changes in encoding quality
are visually annoying to users, automatically switched optical
networks (ASONs) in which there is a cost for re-establishing
a lightpath [31], and power generation with dynamic demand,
since the cheapest types of generators typically have very high
switching costs [32].
E. Performance metric
In order to evaluate the performance of the online algo-
rithms we discuss, we focus on the standard notion of the
competitive ratio. The competitive ratio of an algorithm A is
defined as the maximum, taken over all possible inputs, of
cost(A)/cost(OP T ), where cost(A) is the objective function
of (4) under algorithm A and OP T is the optimal offline
algorithm. In the general context, the “inputs” are the functions
{h
t
(·)}, which are able to capture the time-varying workload,
electricity price, propagation delays and so on in our geograph-
ical load balancing problem.
Actually the geographical load balancing problem (3) and
the generalization (4) are instances of the class of problems
known as “Metrical Task Systems (MTSs)”. MTSs have re-
ceived considerable study in the algorithms literature, and it
is known that if no further structure is placed on them, then
the best deterministic algorithm for a MTS has competitive
ratio proportional to the number of system states [33], which
is infinity in our problem.
Note that the analytic results of Section III focus on the
competitive ratio, assuming that the service has a finite dura-
tion, i.e. T < ∞, but allowing arbitrary sequences of convex
functions {h
t
(·)}. Thus, the analytic results provide worst-
case (robustness) guarantees. However, to provide realistic cost
estimates, we also consider case studies using real-world traces
for {h
t
(·)} in Section IV.
III. ALGORITHMS AND RESULTS
We can now study and design online algorithms for geo-
graphical load balancing. We start by analyzing the perfor-
mance of the classic Receding Horizon Control (RHC). This
uncovers some drawbacks of RHC, and so in the second part of
this section we propose new algorithms which address these.
We defer the proofs to Appendix.
A. Receding Horizon Control (RHC)
RHC is classical control policy [16] that has been proposed
for dynamic capacity provisioning in data centers [14], [15].
Informally, RHC works by, at time τ, solving the cost
optimization over the window (τ, τ +w) given the starting state
x
τ −1
. Formally, define X
τ
(x
τ −1
) as the vector in (R
S
)
w+1
indexed by t ∈ {τ, . . . , τ + w}, which is the solution to
min
x
τ
,...,x
τ +w
τ +w
X
t=τ
h
t
(x
t
) +
τ +w
X
t=τ
d(x
t−1
, x
t
) (6)
subject to 0 ≤ x
t
∈ R
S
.
Algorithm 1 (Receding Horizon Control: RHC). For all t ≤
0, set the number of active servers to x
RHC,t
= 0. At each
timeslot τ ≥ 1, set the number of active servers to
x
RHC,τ
= X
τ
τ
(x
RHC,τ −1
). (7)
In studying the performance of RHC there is a clear divide
between the following two cases:
1) The homogeneous setting (S = 1): This setting considers
only one class of servers, and thus corresponds to a single
data center with homogeneous servers. Under this setting,
only the number of active servers is important, not which
servers are active, i.e., x
t
is a scalar.
2) The heterogeneous setting (S ≥ 2): This setting allows for
different types of servers, and thus corresponds to a single
data center with heterogeneous servers or to a collection
of geographically diverse data centers. Under this setting,
we need to decide the number of active servers of each
type, i.e., x
t
is a vector.
To start, let us focus on the homogeneous setting (i.e.,
the case of dynamic resizing capacity within a homogeneous
data center). In this case, RHC performs well: it has a small
competitive ratio that depends on the minimal cost of an active
server and the switching cost, and decays to one quickly as
the prediction window grows. Specifically:
Theorem 1. In the homogeneous setting (S = 1), RHC is
(1 +
β
(w+ 1)e
0
)-competitive.
Theorem 1 is established by showing that RHC is not
worse than another algorithm which can be proved to be
(1 +
β
(w+ 1)e
0
)-competitive. Given Theorem 1, it is natural to
wonder if the competitive ratio is tight. The following result
highlights that there exist settings where the performance of
RHC is quite close to the bound in Theorem 1.
Theorem 2. In the homogeneous setting (S = 1), RHC is not
better than (
1
w+2
+
β
(w+ 2)e
0
)-competitive.
It is interesting to note that [34] shows that a prediction
window of w can improve the performance of a metrical task
system by a factor of at most 2w. If β/e
0
≫ 1 then RHC
is approximately within a factor of 2 of this limit in the
homogeneous case.
The two theorems above highlight that, with enough look-
ahead, RHC is guaranteed to perform quite well in the ho-
mogeneous setting. Unfortunately, the story is different in
the heterogeneous setting, which is required to model the
geographical load balancing.
Theorem 3. In the heterogeneous setting (S ≥ 2), given any
w ≥ 0, RHC is ≥ (1 + max
s
(β
s
/e
0,s
))-competitive.
In particular, for any w > 0 the competitive ratio in the
heterogeneous setting is at least as large as the competitive
ratio in the homogeneous setting with no predictions (w = 0).
Most surprisingly (and problematically), this highlights that
RHC may not see any improvement in the competitive ratio
as w is allowed to grow.
The proof, given in Appendix D involves constructing a
workload such that servers at different data centers turn on
and off in a cyclic fashion under RHC, whereas the optimal
solution is to avoid such switching. Therefore, {h
t
(·)} result-
ing in bad competitive ratio are not any weird functions but
include practical cost functions for formulation (3). Note that
the larger the prediction window w is, the larger the number
of data centers must be in order to achieve this worst case.
The results above highlight that, though RHC has been
widely used, RHC may result in unexpected bad performance
in some scenarios, i.e., it does not have “robust” performance
guarantees. The reason that RHC may perform poorly in the
heterogeneous setting is that it may change provisioning due
to (wrongly) assuming that the switching cost would get paid
off within the prediction window. For the geographical load
balancing case, the electricity price based on the availability of
renewable power (e.g., wind or solar) may change dramatically
during a shot time period. It is very hard for RHC to de-
cide which data centers to increase/decrease capacity without
knowing the entire future information, thus RHC may have to
change its decisions and shift the capacity among data centers
very frequently, which results in a big switching cost. Notice
that this does not happen in the homogeneous setting where
we don’t need to decide which data center to use, and the new
information obtained in the following timeslots would only
make RHC correct its decision monotonically (increase but
not decrease the provisioning by Lemma 3).
In the rest of this section we propose an algorithm with
significantly better robustness guarantees than RHC.
B. Fixed Horizon Control
In this section, we present a new algorithm, Averaging Fixed
Horizon Control (AFHC), which addresses the limitation of
RHC identified above. Specifically, AFHC achieves a compet-
itive ratio for the heterogeneous setting that matches that of
RHC in the homogeneous setting.
Intuitively, AFHC works by combining w + 1 different bad
algorithms, which each use a fixed horizon optimization, i.e., at
time 1 algorithm 1 solves and implements the cost optimization
for [1, 1 + w], at time 2 algorithm 2 solves and implements
the cost optimization for [2, 2 + w], etc.
More formally, first consider a family of algorithms param-
eterized by k ∈ [1, w + 1] that recompute their provisioning
periodically. For all k = 1, . . . , w + 1, let Ω
k
= {i : i ≡ k
mod (w + 1)} ∩ [−w, ∞); this is the set of integers congruent
to k modulo w + 1, such that the lookahead window at each
τ ∈ Ω
k
contains at least one t ≥ 1.
Algorithm 2 (Fixed Horizon Control, version k: FHC
(k)
). For
all t ≤ 0, set the number of active servers to x
(k)
F HC,t
= 0 . At
timeslot τ ∈ Ω
k
, for all t ∈ { τ, . . . , τ + w}, use (6) to set
x
(k)
F HC,t
= X
τ
t
x
(k)
F HC,τ −1
. (8)
For notational convenience, we often set x
(k)
≡ x
(k)
F HC
.
Note that for k > 1 the algorithm starts from τ = k − (w + 1)
rather than τ = k in order to calculate x
(k)
F HC,t
for t < k.
FHC can clearly have very poor performance. However,
surprisingly, by averaging different versions of FHC we obtain
an algorithm with better performance guarantees than RHC.
More specifically, AFHC is defined as follows.
Algorithm 3 (Averaging FHC: AFHC). At timeslot τ ∈ Ω
k
,
use FHC
(k)
to determine the provisioning x
(k)
τ
, . . . , x
(k)
τ +w
, and
then set x
AF HC,t
=
P
w+1
n=1
x
(n)
t
/(w + 1).
Intuitively, AFHC seems worse than RHC because RHC
uses the latest information to make the current decision and
AFHC relies on FHC which makes decisions in advance, thus
ignoring some possibly valuable information. This intuition is
partially true, as shown in the following theorem, which states
that RHC is not worse than AFHC for any workload in the
homogeneous setting (S = 1 ).
Theorem 4. In the homogeneous setting (S = 1),
cost(RHC) ≤ cost(AF HC).
Though RHC is always better than AFHC in the homoge-
neous setting, the key is that AFHC can be significantly better
than RHC in the heterogeneous case, even when S = 2.
Theorem 5. In heterogeneous setting (S ≥ 2), there exist
convex functions {h
t
(·)} such that
cost(RHC) > cost(AF HC).
Moreover, the competitive ratio of AFHC is much better
than that of RHC in the heterogeneous case.
Theorem 6. In both the homogeneous setting and the hetero-
geneous setting, AFHC is
1 + max
s
β
s
(w+ 1)e
0,s
-competitive.
The contrast between Theorems 3 and 6 highlights the
improvement AFHC provides over RHC. In fact, AFHC has
the same competitive ratio in the general (possibly heteroge-
neous) case that RHC has in the homogeneous case. So, AFHC
provides the same robustness guarantee for geographical load
balancing that RHC can provide for a homogeneous local data
center.
IV. CASE STUDIES
In the remainder of the paper, we provide a detailed study
of the performance of the algorithms described in the pre-
vious section. Our goal is threefold: (i) to understand the
performance of the algorithms (RHC and AFHC) in realistic
settings; (ii) to understand the potential environmental benefits
of using geographical load balancing to implement “follow
the renewables” routing; and (iii) to understand the optimal
portfolio of renewable sources for use within an Internet-scale
system.
A. Experimental setup
This study uses the setup similar to that of [10], based on
real-world traces for data center locations, traffic workloads,
0 6 12 18 24 30 36 42 48
0
0.2
0.4
0.6
0.8
1
hour
workload (normalized)
(a) Trace 1
0 6 12 18 24 30 36 42 48
0
0.2
0.4
0.6
0.8
1
hour
workload (normalized)
(b) Trace 2
Fig. 1. HP workload traces.
renewable availability, energy prices, etc, as described below.
2
1) The workload: We consider 48 sources of requests, with
one source at the center of each of the 48 continental US states.
We consider 10-minute time slots over two days.
The workload λ
t
is generated from two traces at Hewlett-
Packard Labs [6] shown in Figure 1. These are scaled propor-
tional to the number of internet users in each state, and shifted
in time to account for the time zone of that state.
2) The availability of renewable energy: To capture the
availability of solar and wind energy, we use traces with
10 minute granularity from [35], [36] for Global Horizontal
Irradiance (GHI) scaled to average 1, and power output of
a 30kW wind turbine. The traces of four states (CA, TX,
IL, NC) are illustrated in Figure 2. Note that we do not
consider solar thermal, because of the significant infrastructure
it requires. Since these plants often incorporate a day’s thermal
storage [37], the results could be very different if solar thermal
were considered.
These figures illustrate two important features of renewable
energy: spatial variation and temporal variation. In particular,
wind energy does not exhibit a clear pattern throughout the day
and there is little correlation across the locations considered.
In contrast, solar energy has a predictable peak during the day
and is highly correlated across the locations.
In our investigation, we scale the “capacity” of wind and
solar. When doing so, we scale the availability of wind and
solar linearly, which models scaling the number of generators
in a wind farm or solar installation, rather than the capacity of
each. We measure the “capacity” c of renewables as the ratio
of the average renewable generation to the minimal energy
required to serve the average workload. Thus, c = 2 means that
the average renewable generation is twice the minimal energy
required to serve the average workload. We set capacity c = 1
by default, but vary it in Figures 5 and 7.
3) The Internet-scale system: We consider the Internet-
scale system as a set of 10 data centers, placed at the centers
of states known to have Google data centers [38], namely
California, Washington, Oregon, Illinois, Georgia, Virginia,
Texas, Florida, North Carolina, and South Carolina. Data
center s contains M
s
homogeneous servers, where M
s
is set
to be twice the minimal number of servers required to serve
the peak workload of data center s under a scheme which
routes traffic to the nearest data center. Further, the renewable
availability at each data center is defined by the wind/solar
trace from a nearby location, usually within the same state.
2
Note that the setup considered here is significantly more general than that
of [10], as follows. Most importantly, [10] did not model switching costs
(and so did not consider online algorithms). Additionally, the current work
investigates the optimal renewable portfolio more carefully, using multiple
traces and varying the renewable capacity among other things.
