Applications of Utility-theoretic Models in Software Configuration

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Applications of Utility-theoretic Models in
Software Configuration

• Vahe Poladian
• SSSG
• March 14, 2002

2
Actual Chat of Two PDAs, circa 2100
Compumagic My battery lasts 10 times longer
than yours. Ha-ha!
Cybermatic Oh, yea? At least I have a decent
pipe to the net. Hows your museum edition
modem from 1995?
3
Actual Conversation Continued
Marco de Polo Did you get The map to
Monroeville, PA, that I asked for 20 minutes
ago?
Compumagic Hang on, I am in the middle of a
bridge hand here. 10 MB out of a total of 64 GB
downloaded. Waiting to finish.
Marco de Polo What kind of configuration are
you running, anyway? And then to himself Must
have caught a virus. Packed the semi-truck
battery again, did not negotiate a decent net
service, and completely ignoring my utility.
What is with that!
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Why Utility Theory?

• Individuals make decisions to maximize their
  utility given limited resources,
• Utility theory explains such decisions,
• Provides models for determining optimal
  allocation, given knowledge of resource
  constraints, prices, and utility,
• We believe similar models can be applied to the
  problem of optimal software configuration,
  specifically in mobile computing environments.

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Talk Outline

• Utility Theory by Example
• How Utility Theory Applies to Computing
• Related Work
• Issues Specific to Mobile Computing

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Example from Economics

• Limited Resource(s)
• money, 45 dollars of it,
• Goods
• apples and oranges, measured in pounds,
• Prices (resource to good conversion functions)
• 3 for a a pound of apples,
• 5 for a pound of oranges,
• 3apples 5oranges 45,

Feasible Region
Pounds of Apples
Monetary Constraint
Pounds of Oranges
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Example from Economics (contd.)

• Baskets
• Ordered pairs of (pounds of) apples and oranges,
• Utility
• A function from baskets to real numbers
  indicating the value of a basket to user,
• Indifference curves
• Contours that are made up of baskets of equal
  utility,
• Assume that the higher the curve, the better the
  utility,

Contours of Equal Utility (Indifference Curves)
Optimal Point
Number of Apples
Monetary Constraint
Number of Oranges
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Talk Outline

• Utility Theory By Example
• How Utility Theory Applies to Computing
• Related Work
• Issues Specific to Mobile Computing

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Mobile Computing Scenario

• Hand-held computer, with two limited resources
  battery and (flash, small amount of) memory,
• 2 applications that work in disconnected mode
• An e-mail client, a map lookup program,
• Upload e-mail and map data for offline usage,
• Questions
• How to allocate memory between e-mail and map
  data?
• How to divide the battery life between using the
  e-mail application and the map application?

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Computing Problem Mapped to Utility Theory

• Limited Resources
• Memory and energy,
• Services (similar to goods)
• E-mail and map, measured in number of e-mails
  read /written and number of locations looked up,
• Resource to service conversion functions
  (prices)
• How much memory and energy needed for processing
  a specific number of e-mails?
• For looking up a given number of locations?

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Computing Problem Mapped to Utility Theory
(contd.)

• Baskets
• Ordered pairs of (number of) e-mails processed
  and locations looked up,
• Utility
• A function from baskets to real numbers showing
  value of basket to user,
• Indifference curves
• Lookupsß Email(1-ß) const,

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Insights

• At the optimal point not every resource is
  exhausted,
• The optimal point depends on the shape and
  position of the indifference curves not just
  the resource constraints,
• This resembles linear / convex programming,
• Quantities involved (pounds of apples, oranges)
  need not be continuous, and can be discrete,
  yielding an integer programming problem,

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Talk Outline

• Utility Theory By Example
• How Utility Theory Applies to in Computing
• Related Work
• Issues Specific to Mobile Computing

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Related Research

• The Amaranth project
• Q-RAM, QoS-based Resource Allocation Model,
• Chen Lee thesis and work leading to it,
• Thesis of S. Khan from the University of
  Victoria,
• I present here a portion of Chen Lees work,

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Problem Definition

• Given
• A computing machine with limited resources, such
  as CPU, memory, network bandwidth,
• Software applications that offer services.
  Applications are configurable and can provide
  various service quality and resource usage
  trade-offs,
• The space of configurations of the system, where
  a configuration of the system is a snap-shot such
  that the quality of service of each application
  is fixed to a particular level,
• The utility of a user with for each
  configuration,
• Determine
• A configuration of the system that maximizes the
  users utility, while satisfying the resource
  constraints,

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Chen Lee Approach

• Proposes and tackles the discrete version of the
  problem,
• Assumes that utility is increasing with respect
  to the quality level of a single service,
• Does not assume that the relationship between the
  quality space and resource space is functional,
  i.e., allows the possibility that a given
  configuration (basket) can generally be achieved
  by more than one resource combination,
• Observes that the entire quality space, i.e. the
  space of all the configurations or baskets, is a
  Cartesian product of the points in individual
  quality dimensions,
• Samples a small number of points of the utility
  with respect to individual quality dimensions,
• Uses a function (e.g., simple addition, weighted
  addition) to combine utility values from all the
  dimensions,

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Chen Lee Solution

• Shows that the problem is equivalent to an
  integer programming problem,
• Proves that the problem reduces to the 0-1
  knapsack problem, which is NP-hard. Thus, all
  known optimal solutions must be exponential in
  the size of the problem,
• Proposes fast approximation algorithms, that
  yield solutions close to the optimum,
• Separately considers the case of one resource
• Dynamic programming algorithm,

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Dynamic Programming Solution

• Partition the total amount R of the resource into
  small, equal portions R/M each (e.g., M can be
  100). Start with one application, and bring in
  applications one by one,
• Let v(j, k) be the maximum utility achievable
  when only first j applications are considered,
  and the amount of resource available is only k
  R/M,
• Then v(j, k) can be described by considering
  v(j-1,), by considering all allocation choices
  for application number j,

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Dynamic Programming Illustrated
100 ?
?
1 ?
0 ?
1 2 3
Percentage of Resource, k
Applications considered, j
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Dynamic Programming Property

• Dynamic programming has a property
• The search space can be re-used when a change
  occurs in the environment
• in particular, when a new application is brought
  into the system, computing the new optimal
  configuration is fast,
• This is desirable in mobile computing
  environments, where changes in the resources or
  utility necessitate frequent re-configuration of
  the system,

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Solving the General Case

• Dynamic Programming Solution,
• Solution using an Integer Programming package
• using branch and bound method by giving a
  heuristic,
• Approximation algorithm using local search
  technique,

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Talk Outline

• Utility Theory By Example
• How Utility Theory Applies to in Computing
• Related Work
• Issues Specific to Mobile Computing

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Interesting Problems in Mobile Computing

• Solving implementation issues specific to mobile
  computers
• Profiling resource usage. Ensuring that the
  applications actual resource usage numbers
  conform to the advertised values,
• Ensuring that the overhead of the solution is not
  too large,
• Sampling users utility,
• Recently started work on these within the context
  of project Aura
• Characterizing forms of utility curves that arise
  in mobile environments,

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Interesting Problems in Mobile Computing (contd.)

• Dynamically reconfiguring the system after a
  change in the environment, in resources, or
  utility,
• Changes are frequent, as environment is highly
  volatile,
• Despite changes, continuity for users tasks need
  to be provided, and distraction to the user needs
  to be accounted for
• If increase in resource allows a better version
  of an application to be run instead of the
  currently running version, should we switch, or
  is the overhead of switching and distraction to
  the user too much,
• Computational resources of mobile computers are
  limited, hence we are particularly interested in
  solutions that allow fast computation of a new
  optimal configuration after a change
• Tap the optimizations research literature for
  solutions that allow re-using part of the
  computation of an existing configuration in
  computing the new optimal configuration,

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STOP

• Questions, ideas, comments?

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Bonus Slide 1 Q-RAM Approach

• Assume two quality dimensions, p and q. Let (p,
  q) denote a point in the quality hyperspace,
• Assume two resources, r and t. Let r, t denote
  a point in the resource hyperspace,
• Same quality point, e.g. (10, 20) can be achieved
  by multiple resource points, e.g., 3, 5, 5,
  3, 4, 4,
• Suppose 3, 5 can also satisfy (24, 7) and (17,
  11). Of those three points in the quality
  hyperspace, choose the one with highest utility.
  Define a function g(3, 5) max (u((p, q)),
  s.t 3, 5 satisfies (p, q)),
• Take the convex hull of that function,