Open Positions: I am looking for PhD students with strong mathematical background and creativity, who like to prove theorems.

Introduction for students:

Unlike many theoretical computer scientists, my analysis is based on stochastic (probabilistic) models of computer systems. There is no "adversary" sending us worst-case inputs. By contrast, there is a stream of requests, whose arrival times and service demands come from empirically fitted distributions. These distributions might be correlated, and they often exhibit heavy tailed service demands and high variability.

I believe that many conventional wisdoms on which we base computer system designs are not well understood and sometimes false, leading to inferior designs. My research revisits very classic questions in system design. Here are a few examples of commonly-held beliefs that my research challenges:

• Thousands of "load balancing" heuristics do exactly that -- they aim to balance the load among the existing hosts. But is load balancing necessarily a good thing?

• Ever notice that the optimal scheduling policy, Shortest-Remaining-Processing-Time-First (SRPT), is rarely used in practice? There's a fear that the big jobs will "starve", or be treated unfairly as compared with Processor-Sharing (PS). But is this a reality?

• To minimize mean waiting time in a server farm, research suggests that each job should be sent to the server at which it will experience the least wait. That seems good from the job's perspective, but is the greedy strategy best for the system as a whole?

• Given a choice between a single machine with speed s, or n identical machines each with speed s/n, which would you choose? Think again ...

• Migrating active jobs is generally considered too expensive. Killing jobs midway through execution and restarting them from scratch later is even worse! Says who?

• Cycle stealing (using another machine's idle cycles to do your work) is a central theme in distributed systems and has been the topic of thousands of papers. But can we quantify when cycle stealing pays off, as a function of switching costs and threshold parameters?

• Redundancy is the idea of making multiple copies of the same job, where each copy is dispatched to a different queue, and where one only needs to wait for the first copy to complete. When does redundancy help?

Research Specifics:

I work on the design and performance analysis of computer systems including both theory and implementation:

Theoretical work on Algorithms and Analysis: Queueing behavior and stochastic analysis of resource allocation in distributed computer systems. Load sharing policies, routing policies, cycle stealing, replication algorithms, power-efficient policies, threshold policies, and multi-class/multi-server prioritization. Fairness metrics in scheduling. Correlated arrival processes, and analysis under high-variability workloads. Known for ``All-Can-Win Theorem'', demonstrating that scheduling policies which are biased towards favoring small jobs can also be preferable to large jobs.

Stochastic Analysis & Queueing Techniques: : Developing new methods for stochastic analysis. Examples include: (i) Recursive Dimensionality Reduction (RDR), a technique that allows one to reduce a Markov chain that grows unboundedly in many dimensions to a Markov chain that grows unboundedly in only one dimension, by using the idea of busy period transitions; (ii) Recursive Renewal Reward (RRR) and Clearing Analysis on Phases (CAP) , techniques that allow one to obtain closed-form solutions for many one-dimensional infinite repeating Markov chains, including the M/M/k with setup chain; (iii) Exact analysis of Replication Systems: the first exact solution (in product-form) for replication systems, involving any number of servers, and number of classes, and any degree of replication.

Computer systems implementation: Resource management in data centers and other distributed systems. Implementation of QoS tail latency guarantees for flows in networked storage systems, based on techniques from Deterministic Network Calculus and Stochastic Network Calculus (PriorityMeister and SNC-Meister). Online scheduling of jobs with heterogeneous preferences in data centers with heterogeneous servers (TetriSched). Dynamic power management in multi-tier data centers (AutoScale). Scheduling of Memory Controllers (ATLAS). Pricing and queueing optimizations for cloud services. Kernel-level connection scheduling in Web servers. Solutions for coping with transient overload in Web servers. QoS for e-commerce applications involving the backend database. Prioritization mechanisms for OLTP transactions in database servers. Job scheduling in supercomputing centers.

Modeling and Workload characterization: Known for the discovery of Pareto heavy-tailed distribution of UNIX process CPU lifetimes. Statistical characterization of workloads including UNIX processes, web, OLTP, supercomputing, memory workloads, and parallel jobs.

My TENURE RESEARCH STATEMENT from May 2007:

• Introduction
• Sec 1: The SYNC Project: Scheduling Your Network Connections -- Why Favoring Short Jobs Helps All Jobs
• Sec 2: Computer Systems with Fluctuating Load
• Sec 3: QoS for Database Management Systems
• Sec 4: User Behaviors: Dangers of Closed versus Open Workload Generators
• Sec 5: Routing for Server Farms with Highly-Variable Job Sizes
• Sec 6: Cycle Stealing, Threshold-Based Sharing, and Other 2D-Infinite Chains
• Sec 7: Priority Queueing and Capacity Planning for Server Farms
• Sec 8: Auction-Based Scheduling for the TeraGrid