Balancing Risk and Reward in a Balancing Risk and Reward in a Market-based Task ServiceMarket-based Task Service

David Irwin, Laura Grit,

Jeff Chase

Department of Computer ScienceDuke University

Resource Management in the LargeResource Management in the Large

Grids enable resource sharing• Each user has ability to use more resources

• Requires global coordination of resource sharing

Current technology: private grids (Virtual Organizations)

Next generation: public Grid• Larger scale of resources and participants

• Dynamic collection suppliers and consumers

• Varying supply and demand

Market-based approaches are attractive• Decentralized resource management

• Independent actors acting on self-interest produce desired global outcomes

e.g. Spawn, Mariposa, G-commerce framework, Nimrod-G

• Increasingly important as we move to larger grids

Example: Market-Based Task ServiceExample: Market-Based Task Service

Tasks are batch computation jobs• Self-contained units of work

• Execute anywhere

• Consume known resources

Characteristics of a market-based task service• Tasks deliver value when they complete

• Negotiation between customers and task service sitesValue (price) and quality of service (completion time)

• Form contracts for task executionBreach of contract implies a penalty

• Consumers look for the best deal; sites maximize their profits

Customer

Task Service Sites

Bid (value, service demand)

Accept (completion time, price)

Accept (contract)

Bid (value, service demand)Reject

Bid (value, service demand)

Reject

Accept (completion time, price)

Market FrameworkMarket Framework

Goals and Non-goalsGoals and Non-goals

Goals

• Define profit-maximizing heuristics for acceptance (admission control) and scheduling for task service sites

Which tasks should a site accept? When? For how much?

• Financial metaphor: balance risk and reward subject to user bids that trade off price and quality of service

Non-goals

• Other pieces for a fully functioning economyHow is currency supplied and replenished?

How to make payments and enforce contracts?

How to propagate price signals to buyers?

What incentive mechanisms will induce truthful user bids?

OutlineOutline

Overview• Motivation and Goals/Non-goals

• Task Services

Background• Specifying user bids

• Problem Statement

Heuristics

• Methodology

• Present Value and Opportunity Cost

• Negotiation and Admission Control

Conclusions

Specifying User Bids and ContractsSpecifying User Bids and Contracts

Negotiation establishes agreement on price and service quality

Use value functions giving an explicit mapping of service quality to value

• Need a representation that is simple, rich, and tractable

• Millennium: linearly decaying value functions [Chun02]

Delayed tasks decay at constant rate of decayi (urgency)

Extend functions to include penalties

• May specify an optional bound on a penalty

Penalties expire at time expirei

Time

Val

ue

RuntimeMaximum Value

Decay at constant rate decayi

Penalty

Example Value FunctionExample Value Function

Problem StatementProblem Statement

Based on user bids we must decide…• Admission control: which tasks to commit to?

• Scheduling: when to run a task?

Schedule accepted tasks to maximize value

• How much to charge for tasks?

Price to service quality tradeoff specified in value functions

Problem extends classical value-based scheduling problems• Total Weighted Tardiness and Total Weighted Completion Time

NP-hard for off-line instances; problem is difficult

• Examine on-line instances of the problem: need heuristics

• Site can negotiate for higher value or reject some tasks

Server Scheduling HeuristicsServer Scheduling Heuristics

Discounting future gains

• Bias schedule for shorter tasks

• Realizing gains quickly may be more important than value

Accounting for opportunity cost

• Bias towards high urgency tasks

• Account for losses in other tasks from a scheduling decision

Admission control

• High valued tasks earn value for the system

• High urgency tasks constrain the future task mix

Experimental MethodologyExperimental Methodology

Develop heuristics to maximize value and opportunity cost• Heuristics have multiple components

Evaluate in on-line open market setting• Schedule varying task mixes over emulated batch task engine

• Evaluate components in isolation and combination

• Compare with Millennium FirstPrice policy

Generated workloads to drive task sites

• Explore different areas of the parameter space

Focus on relative value and sensitivity analysis

Workload ConsiderationsWorkload Considerations

Workload characteristics • Arrival and cost distributions representative of real batch workloads as

characterized by previous studies

Exponential inter-arrival times and durations [Downey99]

• Previous studies give little guidance on how users value their jobs

Distribution of value and urgency similar to Millennium study [Chun02]

Adapt bimodal distributions for value and urgency

Characterize by skew ratios: ratio of high/low means

Magnitude of results dependent on workload characteristics• Results are conservative: look at stable markets

Discounting Future GainsDiscounting Future Gains

Account for risk of deferring future gains• Example: Given two tasks with same unit gain and urgency it is

preferable to run shorter task firstShorter tasks carry lower risk of preempting newly arriving tasks

• Risk-averse scheduler may choose to run lower-yield task if it can realize gains quickly

Approach based on notion of present value common in finance• PVi = yieldi / (1 + (discount_rate * RPTi))

• PVi represents investment value

Earning simple interest at discount_rate for RPTi

• Higher discount_rate results in more risk-averse system

Present value heuristic (PV) selects jobs in order of discounted unit gain• PVi/RPTi

Improvement vs. Discount RateImprovement vs. Discount Rate

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0.001 0.01 0.1 1 10

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irstP

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Discount Rate (%)

Value Skew Ratio=9Value Skew Ratio=4

Value Skew Ratio=2.15Value Skew Ratio=1.5

Value Skew Ratio=1FirstPrice

Opportunity CostOpportunity Cost

Extend heuristic to consider opportunity cost• Losses occurring from choosing task i instead of task j, causing task j

to decay in value

• Opportunity cost depends only on the urgency of competing tasks

Opportunity Cost:

• Bounded penalties requires O(n2) to compute least cost task

• We can simplify with unbounded penalties

Takes O(log n) to compute least cost task

• Equivalent to Shortest Weighted Processing Time First (SWPT)

),(*;0

j

ijj

ijj expireRPTMINdecaycost

Balancing Gains and Opportunity CostBalancing Gains and Opportunity Cost

Risky to defer gains on basis of opportunity cost alone• FirstReward metric combines task gains with opportunity

cost

rewardi = ((α)*PVi – (1-α)*costi)/RPTi

• α controls degree to which system considers expected gains

With α=1 and discount_rate = 0 rewardi reduces to

FirstPrice

With α=0 rewardi reduces to a variant of SWPT

Bounded: Improvement vs. Risk/Reward WeightBounded: Improvement vs. Risk/Reward Weight

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

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irstP

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(%)

Risk versus Reward weight (Alpha)

Decay Skew Ratio=5Decay Skew Ratio=7Decay Skew Ratio=3

It is useful to consider value: high α biases against low-valued jobs, which tend to reach their bounds faster

Unbounded: Improvement vs. Risk/Reward WeightUnbounded: Improvement vs. Risk/Reward Weight

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

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Risk versus Reward Weight (Alpha)

Decay Skew Ratio=7Decay Skew Ratio=5Decay Skew Ratio=3

Little benefit in considering gains with unbounded penalties

Negotiation and Admission ControlNegotiation and Admission Control

Each site may accept or reject a task• Accepted tasks negotiate to establish a price and expected completion

time

Admission control procedure• Integrate task into current schedule according to heuristic

• Determine expected yield for task if completed

• Apply acceptance heuristic to determine acceptance

• If task is profitable then accept the bid and issue a server bid to client

• If client accepts the contract then execute the task

Later arrivals could delay task beyond its expected completion time

Admission Control HeuristicAdmission Control Heuristic

Acceptance Heuristic

• Consider potential reward and constraining future task mix

• Urgent tasks incur more risk

Heuristic based on task’s slack

• Slack is the amount of additional delay that the task can incur before its reward falls below some yield threshold

Slacki = (PVi – costi)/decayi

• Policy rejects tasks whose slack falls below some slack threshold

Slack captures the risk of accepting tasks as determined by its decay rate and position in the schedule

Improvement vs. Admission ThresholdImprovement vs. Admission Threshold

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-200 -100 0 100 200 300 400 500 600 700

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sion

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trol

(%)

Admission Control Threshold

Load=2Load=1.33Load=0.89Load=0.67Load=0.50

ConclusionsConclusions

Develop heuristics for market based task scheduling and admission control

Bids capture both user value and urgency

• Approach based on a financial metaphor

• Cost and risk often more important than gains

Heuristics that consider gains are effective in some cases

Contributions• Detail different areas of scheduling risk

• Explore parameter space for a general scheduling heuristic

• Show how value-based schedulers can drive server bidding and admission control in a computational economy

QuestionsQuestions

Simplifying System AssumptionsSimplifying System Assumptions

System setting

• Homogeneous processors

• Preemption enabled; suspended tasks resumed on any processor

• System never schedules a job with less than its full resource request

• Predicted service demand is accurate

• No interference due to network, memory, or storage contention

Future WorkFuture Work

Further study of market dynamics

Task services participate in a service market

• User utility functions may be used in an underlying resource market

How do services operate in a commodities market?

• Services must buy and sell resources

Yield Rate vs. Load FactorYield Rate vs. Load Factor

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0.5 1 1.5 2 2.5 3 3.5 4 4.5

Ave

rage

Yie

ld R

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Load Factor

FirstReward, Alpha=0FirstReward, Alpha=0.2FirstReward, Alpha=0.4FirstReward, Alpha=0.6FirstReward, Alpha=0.8

FirstReward, Alpha=1FirstPrice w/o Admission Control

Service MarketsService Markets

Consider task service as part of a Service Market

• Sites sell a service

Service quality and/or price varies according to system conditions

Sites distributed across the Grid

• Service abstracts the physical resources Client bids based on meaningful performance

measures (i.e. response time)

• Clients negotiate contracts that incorporate measures of service quality and assurance as well as price

Clients pay more for better service

Services may incur a penalty if contracts are not honored