Runtime adaptation of queued networks through dynamic programming

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Runtime adaptation of queued networks
throughdynamic programming

• Assel Akzhalova, Iman Poernomo, Mahbub Gani
• Kings College London
• http//www.palab.kcl.ac.uk

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Objective

• To develop controllers for changing QoS
  parameters at runtime by means of classical
  control theory

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Queues and QoS modelling

• We use Queue Network System (open)
• For many applications, queueing network models
  achieve a favorable balance between accuracy and
  efficiency.
• They can be defined, parameterized, and evaluated
  at
• relatively low cost.
• It can be used at runtime to determine
  complicated QoS characteristics

1999 Menascé.
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Queues and QoS modelling

• The allocation of resource problem - to provide
  an agreed quality of service (QoS) is actually
  load-balancing problem or typical optimal control
  problem.
• Some types of load-balancing problems 2
• Routing or job allocation
• Server allocation
• Scheduling or the order of serving

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Queues and QoS modelling

• Examples
• In 3 the objective is to find a workload
  allocation in cluster that minimizes mean
  response time
• The optimization model is to minimize a weighted
  sum of total machines while satisfying the
  average response time constraint for multi-tier
  server network.4
• The optimal switching policy is obtained
  numerically by solving a dynamic programming
  equation. 5

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Formal statement of problem
We now consider queued networks that can evolve
over discrete time. The self-adapted system
strategy is to reconfigure the system during
run-time execution to be as near as possible to
desirable response time RTdes with minimum total
processing cost of the system. In a QoS-aware
SOA, instantiation might involve
searching directories for equivalent services and
determining the best candidate based on QoS
information.
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Possible connections
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Denotations
The ancestor(s) function tells us what service
(if any) calls s and what type of communication
connection is used.
Each Mi denotes a set of functionally equivalent
services that implement the abstract
functionality defined by service si.
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Parameters

• We assume that each service implementation has an
  associated cost
• Additional constraints

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Back to possible connections
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State equations

• We introduce ui(t) function.
• The ui(t) function tells us what service from
  Mi(t) has been allocated to instantiate si in the
  queued network.
• State equations
• (3)
• t 0, . . . , T -1, i 1, 2, ..., n, j 1,
  ...,m
• (4)

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The problem of optimal adaptation

• The problem of optimal adaptation at time t is
  one of finding the best function
• set ui(t) that provides the lowest overall cost
  while meeting the required QoS
• constraints.

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Optimal control problem

• the average response time of the system
• admissible controls
• the cost incurred at time t

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Optimal control problem

• The expected cost of the system
• (12)
• Our objective is to find optimal policy u(t)
  that minimizes the expected cost of the system.
• Our solution is to use dynamic programming
  technique.6

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Dynamic programming technique
We start with an initial guess about the optimal
policy We continue backwards, for tT-1,
T-2,,0 solving Bellmans equation From
Bellmans equation we thus determine functions
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Dynamic programming technique

• Then , generated at the last
  step is equal to the optimal cost.
• The sequence of found policies
  
• is also optimal.

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Algorithm
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General solution
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Example
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Example
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Example
We used arrival rate with Poisson distribution
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Example
Response time of the system
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Cost for each components
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Self-adaptive systems

• Self-adaptive systems are capable of changing
  their behavior at runtime to meet target
  behavioral constraints
• Advantages
• They provide dependable services to clients
• They reduce the strong dependence on human
  resources
• They react to different events more quickly

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Self-adaptive systems

• A typical example

Denial of Service Prevention (Sysmaster
product) http//www.sysmaster.com/s_net_qos.htm
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Another examples

• Data Centres, Clusters and GRID Computing
  Systems, Cloud computing
• The typical problem here is the allocation of
  resource as to provide an agreed quality of
  service (QoS)

Nimrod/G - http//www.csse.monash.edu.au/davida/n
imrod/nimrodg.htm
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The first step - previous work (Palab)

• Example 7 changing a queue service rate
  pre-emptively in response to a prediction that
  utilization heads toward instability.

• G is the controlling function
• W is the component
• H is the ARMA prediction engine

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The next step - adaptation engine

• We are investigating classical control theory to
  develop controllers for changing QoS parameters
  at runtime 8

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Adaptation engine

• Self-adaptive software use policies to decide how
  to react to monitored events
• In 9 it was built the policy for self-adaptive
  software as one independent level on top of
  software architecture

Qianxiang Wang, 2005
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Another examples

• In the video application clients may request more
  network resources for a running session, in order
  to receive better video quality.
• The authors use Ponder, a declarative,
  object-oriented language for specifying security
  and management policies for distributed systems.
  10

2003, Leonidas LymberopoulosEmil Lupu, and
Morris Sloman
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Summary

• Self-adaptive systems
• Queues and QoS modelling
• Formal statement of problem
• Dynamic programming technique
• Solution
• Future work

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References

• Menascé 1999
• Onno Bohma, Ger Cool, and Zhen Liu Queuing
  Theoretic solution methods for models of parallel
  and distributed systems // INRIA, 1996, 23 p
• Alex Zhang, Pano Santos, Dirk Beyer, Hsiu-Khuern
  Tang Optimal Server Resource Allocation Using an
  Open Queueing Network Model of Response Time //
  Intelligent Enterprise Technology Laboratory HP
  Laboratories Palo Alto HPL-2002-301, 2002
• Ligang He, Stephen A. Jarvis, David Bacigalupo,
  Daniel P. Spooner, Xinuo Chen and Graham R. Nudd
  Queueing Network-based Optimisation Techniques
  for Workload Allocation in Clusters of
  Computers// Proceedings of the 2004 IEEE
  International Conference on Services Computing
  (SCC04)
• J. Palmer, I. Mitrani Optimal andheuristic
  policies for dynamic server allocation // J.
  Parallel Distrib. Comput. 65 (2005) 1204 1211

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References

• Dmitri P. Bertsecas Dynamic programming and
  optimal control 2006
• Nurzhan Duzbayev, Iman Poernomo, Runtime
  Prediction of Queued Behaviour, QoSA 2006
• Assel Akzhalova, Nurzhan Duzbayev, Model Driven
  Control, JOT December 2007
• Qianxiang Wang Towards a Rule Model for
  Self-adaptive Software, ACM SIG-SOFT Software
  Engineering Notes, January 2005, Volume 30,
  Number 1, p.1-5
• Leonidas Lymberopoulos,Emil Lupu, and Morris
  Sloman An Adaptive Policy-Based Framework for
  Network Services Management // Journal of Network
  and Systems Management, Vol. 11, No. 3, September
  2003, p. 277-303

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Questions
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Thank you