Single machine scheduling problems with uncertain parameters and the OWA criterion

In this paper a class of single machine scheduling problems is discussed. It is assumed that job parameters, such as processing times, due dates, or weights are uncertain and their values are specified in the form of a discrete scenario set. The Ordered Weighted Averaging (OWA) aggregation operator is used to choose an optimal schedule. The OWA operator generalizes traditional criteria in decision making under uncertainty, such as the maximum, average, median or Hurwicz criterion. It also allows us to extend the robust approach to scheduling by taking into account various attitudes of decision makers towards the risk. In this paper a general framework for solving single machine scheduling problems with the OWA criterion is proposed and some positive and negative computational results for two basic single machine scheduling problems are provided

Scheduling over Scenarios on Two Machines

We consider scheduling problems over scenarios where the goal is to find a single assignment of the jobs to the machines which performs well over all possible scenarios. Each scenario is a subset of jobs that must be executed in that scenario and all scenarios are given explicitly. The two objectives that we consider are minimizing the maximum makespan over all scenarios and minimizing the sum of the makespans of all scenarios. For both versions, we give several approximation algorithms and lower bounds on their approximability. With this research into optimization problems over scenarios, we have opened a new and rich field of interesting problems.Comment: To appear in COCOON 2014. The final publication is available at link.springer.co

Efficient Task Replication for Fast Response Times in Parallel Computation

One typical use case of large-scale distributed computing in data centers is to decompose a computation job into many independent tasks and run them in parallel on different machines, sometimes known as the "embarrassingly parallel" computation. For this type of computation, one challenge is that the time to execute a task for each machine is inherently variable, and the overall response time is constrained by the execution time of the slowest machine. To address this issue, system designers introduce task replication, which sends the same task to multiple machines, and obtains result from the machine that finishes first. While task replication reduces response time, it usually increases resource usage. In this work, we propose a theoretical framework to analyze the trade-off between response time and resource usage. We show that, while in general, there is a tension between response time and resource usage, there exist scenarios where replicating tasks judiciously reduces completion time and resource usage simultaneously. Given the execution time distribution for machines, we investigate the conditions for a scheduling policy to achieve optimal performance trade-off, and propose efficient algorithms to search for optimal or near-optimal scheduling policies. Our analysis gives insights on when and why replication helps, which can be used to guide scheduler design in large-scale distributed computing systems.Comment: Extended version of the 2-page paper accepted to ACM SIGMETRICS 201