Deadline Scheduling and Heavy tail distributionS

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Presentation transcript:

Deadline Scheduling and Heavy tail distributionS Lang Tong School of Electrical and Computer Engineering Cornell University, Ithaca, NY 14850

Overview What am I working on What do I intend to work on Deadline scheduling with outsourcing options: algorithms and performance analysis Worst-case optimal deadline scheduler What do I intend to work on Investigate impacts of multivariate heavy tail distribution on deadline scheduling performance

Deadline scheduling and outsourcing Key characteristics: Jobs with different sizes, deadlines, and rewards Multiple local inexpensive servers with varying capacities Expensive outsourcing options Scheduling actions: Admission: whether to take on a job Scheduling: which server should be assigned Outsourcing: whether and when to outsource

Applications Scheduling for distributed resources in cloud

Jobs with deadlines

Profit = Revenue - Cost

Offline deadline scheduling

Online deadline scheduling

Example: earliest deadline first (EDF)

Competitive ratio: online vs. offline

Optimal competitive ratio

EDF under stress

Deadline scheduling with admission control

Maximum competitive ratio

Maximum competitive ratio bounds

Maximum competitive ratio bounds

Insights and intuitions Easy cases: lightly loaded traffic Heavy tailed deadlines, heavy tailed interarrivals. Worst cases: Cascades of heavy tailed jobs. Optimal deadline scheduling Threshold admission control + EDF Load balancing

Converse:

Converse:

Achievability: TAGS Easy job: accept + LLF Difficult job: reward threshold test

Proof sketch:

Some numerical results: light tail jobs Exponential job length, Poisson arrival

Effects of job size Pareto job length, Poisson arrival

Effects of job size and arrival Pareto job length and independent Pareto inter-arrival

Effects of job size Pareto job length and Markov dependent Pareto inter-arrival

Summary remarks Deadline scheduling is a classical problem that arises in many applications with real-time operation constraints. Very little is known about the impact of heavy tailed distributions on performance. We have developed a simple but optimal online scheduling (in competitive ratio) with very good performance in simulations involving heavy tail distributions.