xiaobo zhou department of computer science university of colorado at colorado springs
DESCRIPTION
Robust Processing Rate Allocation with Feedback Control for Proportional Slowdown Differentiation. Xiaobo Zhou Department of Computer Science University of Colorado at Colorado Springs. Outline. Proportional Slowdown Differentiation (PSD) State-of-the-Art An Integrated Approach to PSD - PowerPoint PPT PresentationTRANSCRIPT
1
Robust Processing Rate AllocationRobust Processing Rate Allocationwith Feedback Control for with Feedback Control for
Proportional Slowdown DifferentiationProportional Slowdown Differentiation
Xiaobo ZhouDepartment of Computer Science
University of Colorado at Colorado Springs
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
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 Differentiated Services
(Reservations-based) (relative vs. absolute)
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
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 same-service-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
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
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
It is popular– differentiation predictability– proportional fairness
qi i
qj j = , for all i, j, = 1,2,...,n
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
Response Time vs. Slowdown
Response time – Queueing delay + service time– 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
Client / Incoming link Server / Outgoing linkQueue
Arrival Rate Service Rate
E[W/X] =E[W]W[X-1] E[W]/E[X]
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
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
A Heavy-tailed Distribution The Pareto distribution is a typical heavy-tailed
In practice, there is some upper bound on the maximum size of a job (p) -- Bounded Pareto distribution
kxxkxf ,0k, )( 1
kxpxxkpk
xf
,0k, p)k,,K()/(1
1)( 1 1
f(x)
xpk
Power law w/ exp - -1
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,
.])[1(2
][][][][][
121
XE
xExEXEWESE
p
kpkKkp
pkK
pkKxdxxfXE
1
1
),,()ln(ln),,1(
),,()(][
p
k pkK
pkKdxxxfXE
),,2(
),,()(][ 22
.),,1(
),,()(][ 11
p
k pkK
pkKdxxxfXE
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]
Processing Rate Allocation PSD model
A Proportional Processing Rate Allocation
.Ni1 ))(2
][( ])[(2
][][][
12
bc
bSE
XEc
xExESE
ii
ii
ii
ii
E[Si ] i
E[Si ] j = , for all i, j, = 1,2,...,N
.Ni1 ][ /
][1
1
1
XEXE
c iN
i ii
N
i i
i
ii
.Ni1 )][1(2
/][][][
1
1
12
N
i i
i
N
i iii
XE
xExESE
Simulation ModelProcessing procedure is partitioned into sampling periods
– Request generator– Load estimator– Rate allocator
GNU Scientific library (GSL)
Effectiveness of Rate Allocation
Simulated and expected slowdowns of 2 classes (1: 2= 1:2/1:4)
Effectiveness of Rate Allocation
Simulated and expected slowdowns of 3 classes (1: 2: 2= 1:2:3)
Predictability vs. Variance Percentiles of simulated slowdown ratios for 2 and 3 classes
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%
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
Queueing & Control Integration
Queueing theoretical rate predictorA 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
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) //g is the control gain parameter
Rate allocation adjustment– At the end of sampling period k, the adjustment for k+1 period
– Rate allocation for k+1 period is
)(
)()( 11
kS
kSke
i
i
i
ii
)).(())(
)(()
)1(
)1((
11
kefkc
kc
kc
kci
i
i
i
i
N.i1 ),)(
)((
)(
)(
)1(
)1(
111
kc
kc
kc
kc
kc
kc
i
i
i
i
i
i
A New Simulation Model Integration of queueing and control theory
– Feedback controller– Comparator (sensor/monitor)
Performance Evaulation Sensitivity analyses of the integrated approach
Load:0.4->0.2->0.4
Future Work Evaluate different control techniques Integration of process allocation and admission control
with feedback for robust responsiveness differentiation
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