Applications of Utility-theoretic Models in Software Configuration

1. 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. How’s 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!”

4. 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.

5. Talk Outline • Utility Theory by Example • How Utility Theory Applies to Computing • Related Work • Issues Specific to Mobile Computing

6. 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, • 3*apples + 5*oranges = 45, Feasible Region Pounds of Apples Monetary Constraint Pounds of Oranges

7. 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

8. Talk Outline • Utility Theory By Example • How Utility Theory Applies to Computing • Related Work • Issues Specific to Mobile Computing

9. 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?

10. Number of Map Lookups Done Memory Constraint Line Energy Constraint Line Number of E-mails processed 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?

11. Contours of Equal Utility (Indifference Curves) Number of Map Lookups Done Optimal Point Memory Constraint Line Energy Constraint Line Number of E-mails processed 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,

12. Contours of Equal Utility (Indifference Curves) Number of Map Lookups Done Optimal Point Memory Constraint Line Energy Constraint Line Number of E-mails Processed 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,

13. Talk Outline • Utility Theory By Example • How Utility Theory Applies to in Computing • Related Work • Issues Specific to Mobile Computing

14. 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 Lee’s work,

15. 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 user’s utility, while satisfying the resource constraints,

16. 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,

17. 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,

18. 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,

19. Dynamic Programming Illustrated Percentage of Resource, k Applications considered, j

20. 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,

21. 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,

22. Talk Outline • Utility Theory By Example • How Utility Theory Applies to in Computing • Related Work • Issues Specific to Mobile Computing

23. 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 user’s utility, • Recently started work on these within the context of project Aura • Characterizing forms of utility curves that arise in mobile environments,

24. 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 user’s 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,

25. STOP • Questions, ideas, comments?

26. 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,