Energy Efficient Geographical Load Balancing
via Dynamic Deferral of Workload
Muhammad Abdullah Adnan
Ryo Sugihara (Amazon.com)
Rajesh K. Gupta
Department of CSE
University of California San Diego (UCSD)
Adnan . IEEE CLOUD 2012
1
Data Centers: Energy Consumption
• Energy expenses become
increasingly important
Data Center
– 61 million MWh per year,
costing about 4.5 billion
dollars: Growing very fast
– Millions of dollars for
companies every year
• Increasing energy prices
and rise of cloud computing
– Energy efficient Cloud
• Significant research on
improving energy efficiency
Adnan . IEEE CLOUD 2012
2
Geographical Load Balancing
• Cloud Computing can be utilized for energy efficient
computing.
– Increasing energy prices.
– ability to dynamically track these price variations.
• Geographical Load Balancing techniques have been
suggested for data centers hosting cloud computation
– exploit the electricity price differences across regions.
Adnan . IEEE CLOUD 2012
3
Qureshi et al.
[ACM SIGCOMM 2009]
• Geographical Load Balancing
– reducing the electricity cost in a wholesale market environment.
– Lower electricity bill by adapting the load balancing with dynamic
electricity price variation.
• Electricity Markets
– Day-ahead markets (futures)
• Hourly price predicted for the following day
– Real-time markets (spot)
• Prices are calculated every five minutes, based on actual
conditions, rather than expectations.
Our work
• More volatile – provides opportunities for savings.
Adnan . IEEE CLOUD 2012
4
Buchbinder et al.’s Approach
[IFIP Networking 2011]
• Online algorithms for migrating jobs between data
centers,
– fundamental tradeoff between energy and bandwidth costs.
• Sophisticated methods to reduce the computational
complexity of the proposed heuristics.
• Drawbacks
– Elementary cost vectors
• Large number of iterations
– Discretization of continuous update rule
• Computationally costly
– Bounded Competitive Ratio
• constant/fixed workload - √
• varying workload – x
– No deadline requirement.
Adnan . IEEE CLOUD 2012
5
Liu et al.’s Algorithm
[ACM SIGMETRICS 2011]
• Distributed algorithms for Geographical Load Balancing
– Multiple sources for workload.
– Incorporated capacity provisioning inside data centers
• Only homogeneous servers
• Investigated how renewable energy can be used to lower
the electricity price of brown energy.
• Drawbacks
– No bound on the maximum delay.
– No workload migration.
Adnan . IEEE CLOUD 2012
6
Dynamic Deferral
• Cloud Computing and Mobile Computing
– More and more computation has been outsourced to the cloud.
– Different types of workload
• Delay sensitive, response time/throughput guarantee, Completion
time/deadline requirement.
• Service level agreement (SLA)
– Latency requirement
– Often has some flexibility
• We use the flexibility from different SLAs for geographical
load balancing to reduce energy consumption.
– Defer some of the workload to execute later when electricity
price is low
– Utilize the slackness in the execution of jobs for energy savings.
Adnan . IEEE CLOUD 2012
7
Assumptions
• Temporal and Geographical variation of electricity
prices.
– Variation is unpredictable.
– Migrate jobs between data centers
• cloud service providers have many replication of their data.
• We consider data centers as computation units.
– Homogeneous/heterogeneous
• Workloads arrive at a central dispatcher.
– Dispatcher cannot store workload
– Makes load balancing decision
CLOUD
dispatcher
Adnan . IEEE CLOUD 2012
8
Geographical Load Balancing
migration
j
assignment
zi,j,d,t
i
xi,d,t
Adnan . IEEE CLOUD 2012
9
Model Formulation
• Workload Model
– Workload Lt released at time t has Deadline Dt
• Cost Model
j
zi,j,d,t
i
– Energy cost
xi,d,t
• Proportional to the workload
C i ,t ( y i ,t )   i   i ,t y i ,t
• piecewise linear function
– Bandwidth cost
• Cost of migration
Lt
B i , t ( z i , j , t )  bi , j z i , j , t
Adnan . IEEE CLOUD 2012
t
t+1
……
t+D
10
Model Formulation
• Assumption: uniform deadline
– Deadline is same for all the jobs
• The net amount of workload executed at data
center i at time t
assigned + migrated in - migrated out
n
y i ,t  x i ,t 
D
n
D
  z j ,i , d ,t  d    z i , j , d ,t  d
j 1 d 1
Adnan . IEEE CLOUD 2012
j 1 d 1
11
Offline Formulation
• Future price known => there exists optimal
solution without migration.
– Dispatcher can always make the correct assignment.
Execution cost
Migration cost
Total assignment equals
total released workload
Total migration cannot
exceed total assignment
Adnan . IEEE CLOUD 2012
12
Online Challenges
Decide xt & zt online
0
t
time
• Unpredictable future electricity cost.
– How much to execute at current time?
– How much to defer to execute later?
– How much to migrate and where?
• Future workload is also unknown
– Online algorithm
Adnan . IEEE CLOUD 2012
13
Our Approach
• Decouple migration from assignment.
• @ Dispatcher – Assignment
– based on the current electricity prices and
future price predictions.
• @ DC - Migration Decision
– The predicted electricity prices by the
dispatcher may contain prediction errors.
– Data centers correct that error by migrating
jobs between each other at later time slots.
Adnan . IEEE CLOUD 2012
14
@ Dispatcher – Assignment
• The dispatcher distributes the workload among n data centers.
DC1
Lt
t
t
t+1
……
t+1
t+D
t+D
DC2
t
t+1
t+D
DCn
t
Adnan . IEEE CLOUD 2012
t+1
t+D
15
@ DC
• Adjust assignment with dynamic electricity price
variation.
– Moving workload at earlier time slots.
– Migrating workload between data centers.
Adnan . IEEE CLOUD 2012
16
Formulation w/o Migration
• Workload assigned at later time slots can only
be moved to previous time slots.
Total execution
should be equal
Data Center 1
t
t+1
t+D
t
t+1
t+D
t
t+1
t+D
Data Center 2
Data Center n
unexecuted workload
Adnan . IEEE CLOUD 2012
execution cannot be less
than unexecuted workload
17
Formulation with Migration
• Workload can migrate between data centers
Data Center 1
t
t+1
t+D
t
t+1
t+D
t
t+1
t+D
Data Center 2
Data Center n
unexecuted workload
Adnan . IEEE CLOUD 2012
every data center
does some work
18
@ DC - Migration Decision
+
t
t+1
t+D
t
t+1
t+D
assigned workload
unexecuted workload
+
t
t+1
t+D
Migrated-in workload
t
t+1
t+D
Migrated-out workload
Adnan . IEEE CLOUD 2012
19
How good is the algorithm?
Lemma
No online algorithm has constant competitive ratio with
respect to the offline formulation.
Proof
Adversary Method
βt+i = K’βt
βt = Kβt+D
CASE 1: xD,t ≠ 0
Lt = Lt+1 = M
t
t+1
……
t+D
Competitive Ratio =
t
t+1
t
t+1
……
……
Offline
Online Cost
Offline Cost
= K’/K, arbitrary
t+D
t+D
K’ > K
t
t+1
Adnan . IEEE CLOUD 2012
……
Any Online
t+D
20
How good is the algorithm?
Lemma
No online algorithm has constant competitive ratio with
respect to the offline formulation.
Proof
Adversary Method
βt+i = K’βt
βt = Kβt+D
CASE 2: xD,t = 0
Lt = M
t
t+1
……
t+D
Competitive Ratio =
t
t+1
t
t+1
……
……
Offline
Online Cost
Offline Cost
= K, arbitrary
t+D
t+D
K’ > K
t
t+1
Adnan . IEEE CLOUD 2012
……
Any Online
t+D
21
How good is the algorithm?
• Since the competitive ratio cannot be bounded, we
compare the online algorithm with much simpler online
algorithms.
• Suppose
Online
Prediction
Algorithm
Error
AEM
√
√
AE
√
x
A
x
x
Adnan . IEEE CLOUD 2012
Migration
22
How good is the algorithm?
Lemma
Cost(AEM) ≤ Cost(AE)
•
Proof
Let Δy = amount of migrated workload
y = amount of non- migrated workload
CostAEM(y) = CostAE(y)
•
Data Center 1
t
t+1
t+D
t
t+1
t+D
Migration happens only when
Cost of execution of Δy at earlier time slot + cost
of migration of Δy
≤
Cost of execution of Δy at later time slot
Data Center 2
CostAEM(Δy) ≤ CostAE(Δy)
Data Center n
t
t+1
unexecuted workload
t+D
•
Cost(AEM) = CostAEM(y) + CostAEM(Δy)
≤ CostAE(y) + CostAE(Δy)
≤ Cost(AE)
Adnan . IEEE CLOUD 2012
23
How good is the algorithm?
Lemma
Cost(AEM) ≤ Cost(AE)
+
Lemma
Cost(AE) ≤ (1+ε) Cost(A)
Proof
Prediction error, ε
Predicted price, β’
Actual price, β
β’ – ε ≤ β ≤ β’ + ε
α + β’y
Cost(AE)
Cost(A)
=
Adnan . IEEE CLOUD 2012
α + βy
≤ 1+
ε
β
≤1+ε
24
How good is the algorithm?
Lemma
Cost(AEM) ≤ Cost(AE)
+
Lemma
Cost(AE) ≤ (1+ε) Cost(A)
‖
Theorem
Cost(AEM) ≤ (1+ε) Cost(A)
Adnan . IEEE CLOUD 2012
25
Electricity Price Prediction
• We model future prices within 24-hr time-frame with
Gaussian random variables with
– Means: predicted prices by moving average from current day
prices.
– Variance: estimated from the history by the weighted average
price prediction filter.
• By using two different methods for mean and variance,
we exploit both temporal and historical correlation of
electricity prices.
Adnan . IEEE CLOUD 2012
26
Evaluation - Electricity Price
• Four data centers geographically located at four different locations.
five minute locational marginal electricity prices in real time market on
15th February, 2012 for four different regions.
Adnan . IEEE CLOUD 2012
27
Evaluation - Workload
• Two MapReduce Traces from Facebook
– Cluster of 600 machines over 24 hours.
– Time slot length of 5 minutes because electricity
prices vary with an interval of 5 minutes.
Workload A
Workload B
Adnan . IEEE CLOUD 2012
28
Evaluation - Deadline
• We vary deadline 1-12 slots and compare cost reduction with
respect to the greedy algorithm without deferral by Qureshi et
al.
• Dynamic deferral can provide around 30% cost savings for
deadlines of 12 slots (1 hour) and even for one slot we can
get 5% cost savings.
Workload A
Workload B
Adnan . IEEE CLOUD 2012
29
Evaluation - Deadline
• We compare the total cost from the algorithms AEM and AE.
• The total cost from AEM is always less than the AE as
claimed in Lemma.
• As deadline increases prediction error increases (AE) but cost
decreases (AEM) due to flexibility of migration.
Workload A
Workload B
Adnan . IEEE CLOUD 2012
30
Non-uniform Deadline
• Workload decomposed according to their associated
deadline, Ld,t , 0 ≤ d ≤ D
• Then we replace the release constraints in the formulations by
D
 L d ,t
 Lt
d 0
• Deadline assignment by k-means clustering based on sizes
(map, shuffle and reduce bytes)
15.64% cost reduction for Workload A
9.23% cost reduction for Workload B
Adnan . IEEE CLOUD 2012
31
Summary of Findings
• Formulation for geographical load balancing with
deferral
– Uniform deadline
– Non-uniform deadline
• Characterization of optimal offline solution
• Online Algorithm
– Formulation with migration
– Formulation without migration
• Future work
– Heterogeneity in data centers/cloud.
– Availability of renewable energy.
Adnan . IEEE CLOUD 2012
32
Thank You
?
Adnan . IEEE CLOUD 2012
33