Transcript Anthill: a Framework for the Development of Agent

Robust Processing Rate Allocation
with Feedback Control for
Proportional Slowdown Differentiation
Xiaobo Zhou
Department of Computer Science
University of Colorado at Colorado Springs
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Outline
 Proportional Slowdown Differentiation (PSD)
 State-of-the-Art
 An Integrated Approach to PSD
– Queueing-theoretical processing rate allocation
– control-theoretical feedback control
 Performance Evaluation
 Research Plan
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2
What is Differentiated Services
 Internet Engineering Task Force (IETF), April 1998
www.ietf.org/html.charters/diffserv-charter.html
 The Goal
– To define configurable types of packet forwarding (called Per-Hop
Behaviors, PHBs), which can provide local (per-hop) service
differentiation for large aggregates of network traffic, as opposed to
end-to-end performance guarantees for individual flows
Best-effort services
(Same-service-to-all)
Integrated Services
(Reservations-based)
Differentiated Services
(relative vs. absolute)
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3
Why Differentiated Services
 Network Service Providers want to:
– Offer a scalable service differentiation (defined in SLA’s)
on core routers in stead of current best-effort service
– Improve revenues through premium pricing and
competitive differentiation
 Applications seek better than best effort:
– Bandwidth
– Packet Delay characteristics
– Packet loss characteristics
– Jitter characteristics
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4
End-to-End Differentiation
 Why Service Differentiation on Servers?
– To provide predictable and controllable differentiation
QoS levels to different request classes of clients
– Diverse service expectations and constraints from
Internet applications and users, making the current sameservice-to-all model inadequate and limiting
 End-to-end DiffServ
– Network core:
• Per-hop differentiated queueing delay and loss rate
– Network edge:
• Service differentiation on Servers and Proxies
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5
Models and Properties
 Models:
– Absolute differentiated services: clients receive an absolute
share of resource usages; possible low resource utilization
• For hard real-time applications
– Relative differentiated services: higher classes will receive
relatively better (or no worse) QoS than lower classes
• For soft real-time applications
 Properties:
– Predictability: differentiation schedules must be consistent,
independent of variations of the class workloads
– Controllability: a number of controllable parameters
adjustable for quality differentiation between classes
– Fairness: lower classes not be over-compromised,
especially when workload is low
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6
A Proportional DiffServ Model
 A proportional differentiation model assigns quality factors to
the traffic classes in proportion to their pre-specified
differentiation weights, independent of class workloads
qi
i
qj = j , for all i, j, = 1,2,...,n
 It is popular
– differentiation predictability
– proportional fairness
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7
QoS Metrics on Servers
 Multimedia Applications
– Mutli-dimensional QoS metric
• Responsiveness
• Image size, resolution, formats
• Streaming bandwidth
– Audio sample rate and sample size
– Video frame rate, frame size, and color depth
 Web Applications
– Responsiveness
– Throughput
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Response Time vs. Slowdown


Arrival Rate
Service Rate
Client / Incoming link
Queue
Server / Outgoing link
 Response time
E[W/X] =E[W]W[X-1]
– Queueing delay + service time
 E[W]/E[X]
– Favors requests that need more service time
 Slowdown
– queueing delay / service time
– gives equal weights to requests regardless of service time
– A high slowdown also means a server is heavily loaded
* Clients expect long delay for “large” requests, and anticipate
short delay for “small” requests
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9
State-of-the-Art
 Queueing-delay differentiation
– Strict priority based packet/request scheduling
– Time-dependent priority based request packet/scheduling
 Response time differentiation
– Strict priority based request scheduling
– Adaptive process allocation for proportional differentiation
 Slowdown differentiation
– queueing-theoretical Processing rate allocation
– M/M/1 PS queue for stretch factor differentiation
– M/G_P/1 FCFS queue
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Challenges and Contributions
 A closed form of slowdown for M/GP/1 FCFS Q
 Average slowdown on Task servers
 Processing rate allocation scheme for PSD
 Control-theoretical approach for robust PSD
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A Heavy-tailed Distribution
 The Pareto distribution is a typical heavy-tailed
f ( x)  k  x  1
 , k  0, x  k
 In practice, there is some upper bound on the maximum
size of a job (p) -- Bounded Pareto distribution
1
  1
 1
f ( x) 

k
x

K(

,
k,
p)
x
 , k  0, p  x  k

1  (k / p)
f(x)
Power law w/ exp - -1
p
k
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x
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Preliminary of Slowdown
 Lemma 1
– Given an M/GP/1 FCFS queue on a server, where the arrival
process has rate  and X denotes the Bounded Pareto service time
density distribution. Let W be a job’s queueing delay (W is
indepenent to X from a FCFS queue), and S be its slowdown.
According to Pollaczek-Khinchin Formula,
2
1

E
[
x
]
E
[
x
]
E[ S ]  E[W ]E[ X 1 ] 
.
2(1  E[ X ])
E[ X ]  
K ( , k , p)

 1

f ( x) xdx  
K (  1, k , p)
 1

(ln
p

ln
k
)
K
(

,
k
,
p
)

p
k
p
K ( , k , p)
K (  2, k , p)
K ( , k , p)
f ( x) x 1dx 
.
K (  1, k , p)
E[ X ]   f ( x) x 2 dx 
2
k
E[ X ]  
1
p
k
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Slowdown on a Task Server
 What is a task server?
–
–
–
–
A processing unit, handling a request class in FCFS manner
Let c i be the normalized processing rate of task server i
\sum_{i=1}^{N} c i = 1
0 < c i  1 for 0  i N
A process, a thread, a processor, a server node
 Lemma 2
– Given an M/GP/1 FCFS queue on a task server i with
processing rate. Xi denotes the Bounded Pareto service time
density distribution on the task server:
• E[Xi] = 1/c i E[X]
• E[X2i] = 1/c2 i E[X2]
• E[X-1i] = c i E[X-1]
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Processing Rate Allocation
 PSD model
E[Si ] i
=
, for all i, j, = 1,2,...,N
E[Si ] j
i E[ x 2 ]E[ x 1 ]
i b
E[Si ] 
( E[Si ] 
)
2(ci  i E[ X ])
2(ci  i b)
1  i  N.
 A Proportional Processing Rate Allocation
i 1  i 1 i E[ X ]
N
ci 
i

N
i 1
i /  i
 i E[ X ]
 i E[ x 2 ]E[ x 1 ]i 1 i /  i
1  i  N.
N
E[Si ] 
2(1  E[ X ]i 1 i )
N
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1  i  N.
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Simulation Model
 Processing procedure is partitioned into sampling periods
– Request generator
– Load estimator
– Rate allocator
 GNU Scientific library (GSL)
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Effectiveness of Rate Allocation
 Simulated and expected slowdowns of 2 classes (1: 2= 1:2/1:4)
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Effectiveness of Rate Allocation
 Simulated and expected slowdowns of 3 classes (1: 2: 2= 1:2:3)
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Predictability vs. Variance
 Percentiles of simulated slowdown ratios for 2 and 3 classes
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Microscopic Views
 Queueing-theoretical allocation is based on the average, a
macro-behavior of class load instead of micro-behaviors,
such as experienced slowdowns of individual requests.
50% vs. 90%
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Drawbacks of Q-based Approach
 Queueing theory can be applied to calculate a request
class’s average slowdown based on the allocated
processing rate. However, we cannot control the variance
of slowdown simultaneously
 Processing rate allocation is based on the average load
conditions of classes, instead of per-request experienced
slowdown: macro-behavior vs. micro-behavior
 Load condition is stochastic, it is difficult to accurately
estimate a class’s load based on its history; estimation
errors may cause inaccurate rate allocation in the short
time scales and slowdown deviation between achieved
slowdown ratio and predicted slowdown ratio.
 So, how to improve micro-behavior so more robust?
– Integrating control theory and queueing theory
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Queueing & Control Integration
 Queueing theoretical rate predictor
 A control loop is used for each pair of adjacent classes
– Sensor/monitor measures the achieved slowdown ratio
– Deviation controller adjusts the rate allocation
– Actuator translate the abstract controller output to physical action
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PID Control
 PID (proportional integral derivative) controller
– Simplicity: adjust the rate allocations in proportion to the
difference between the achieved slowdown ratio and desired one
 A linear feedback control function
– f(e i (k)) = g  e i (k)

S (k )
ei (k )  i 1  i 1
i
Si (k )
//g is the control gain parameter
 Rate allocation adjustment
– At the end of sampling period k, the adjustment for k+1 period
c (k  1)
c (k )
( i
)  ( i
)  f (ei (k )).
ci 1 (k  1)
ci 1 (k )
– Rate allocation for k+1 period is
ci (k  1)
c (k )
c (k )
 i
 ( i
),
ci 1 (k  1) ci 1 (k )
ci 1 (k )
1  i  N.
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A New Simulation Model
 Integration of queueing and control theory
– Feedback controller
– Comparator (sensor/monitor)
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24
Performance Evaulation
 Integrated approach vs. queueing-theoretical approach
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Performance Evaulation
 System load is 0.8 and 3: (2 : 1) = 4: (2 : 1)
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Performance Evaulation
 Sensitivity analyses of the integrated approach
Load:0.4->0.2->0.4
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Future Work
 Evaluate different control techniques
 Integration of process allocation and admission control
with feedback for robust responsiveness differentiation
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28
P&P for IDF Applications
 Multi-dimensional Input & Requirements
–
–
–
–
–
Distributed data sources
Different data formats
Different data priority levels
Different decision requirements
Different workload characteristics
 Multi-dimensional Platform and Performance Metric
– Cluster node partitioning
– Performance measurement
– Performance differentiation
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