19,837 research outputs found
Machine Scheduling with Resource Dependent Processing Times
We consider several parallel machine scheduling settings with the objective to minimize the schedule makespan. The most general of these settings is unrelated parallel machine scheduling. We assume that, in addition to its machine dependence, the processing time of any job is dependent on the usage of a scarce renewable resource. A given amount of that resource, e.g. workers, can be distributed over the jobs in process at any time, and the more of that resource is allocated to a job, the smaller is its processing time. This model generalizes classical machine scheduling problems, adding a time-resource tradeoff. It is also a natural variant of a generalized assignment problem studied previously by Shmoys and Tardos. On the basis of integer programming formulations for relaxations of the respective problems, we use LP rounding techniques to allocate resources to jobs, and to assign jobs to machines. Combined with Graham''s list scheduling, we thus prove the existence of constant factor approximation algorithms. Our performance guarantee is 6.83 for the most general case of unrelated parallel machine scheduling. We improve this bound for two special cases, namely to 5.83 whenever the jobs are assigned to machines beforehand, and to (5+e), e>0, whenever the processing times do not depend on the machine. Moreover, we discuss tightness of the relaxations, and derive inapproximability results.operations research and management science;
Scheduling Storms and Streams in the Cloud
Motivated by emerging big streaming data processing paradigms (e.g., Twitter
Storm, Streaming MapReduce), we investigate the problem of scheduling graphs
over a large cluster of servers. Each graph is a job, where nodes represent
compute tasks and edges indicate data-flows between these compute tasks. Jobs
(graphs) arrive randomly over time, and upon completion, leave the system. When
a job arrives, the scheduler needs to partition the graph and distribute it
over the servers to satisfy load balancing and cost considerations.
Specifically, neighboring compute tasks in the graph that are mapped to
different servers incur load on the network; thus a mapping of the jobs among
the servers incurs a cost that is proportional to the number of "broken edges".
We propose a low complexity randomized scheduling algorithm that, without
service preemptions, stabilizes the system with graph arrivals/departures; more
importantly, it allows a smooth trade-off between minimizing average
partitioning cost and average queue lengths. Interestingly, to avoid service
preemptions, our approach does not rely on a Gibbs sampler; instead, we show
that the corresponding limiting invariant measure has an interpretation
stemming from a loss system.Comment: 14 page
Scheduling of data-intensive workloads in a brokered virtualized environment
Providing performance predictability guarantees is increasingly important in cloud platforms, especially for data-intensive applications, for which performance depends greatly on the available rates of data transfer between the various computing/storage hosts underlying the virtualized resources assigned to the application. With the increased prevalence of brokerage services in cloud platforms, there is a need for resource management solutions that consider the brokered nature of these workloads, as well as the special demands of their intra-dependent components. In this paper, we present an offline mechanism for scheduling batches of brokered data-intensive workloads, which can be extended to an online setting. The objective of the mechanism is to decide on a packing of the workloads in a batch that minimizes the broker's incurred costs, Moreover, considering the brokered nature of such workloads, we define a payment model that provides incentives to these workloads to be scheduled as part of a batch, which we analyze theoretically. Finally, we evaluate the proposed scheduling algorithm, and exemplify the fairness of the payment model in practical settings via trace-based experiments
Scheduling Parallel Jobs with Linear Speedup
We consider a scheduling problem where a set of jobs is distributed over parallel machines. The processing time of any job is dependent on the usage of a scarce renewable resource, e.g., personnel. An amount of k units of that resource can be allocated to the jobs at any time, and the more of that resource is allocated to a job, the smaller its processing time. The dependence of processing times on the amount of resources is linear for any job. The objective is to find a resource allocation and a schedule that minimizes the makespan. Utilizing an integer quadratic programming relaxation, we show how to obtain a (3+e)-approximation algorithm for that problem, for any e>0. This generalizes and improves previous results, respectively. Our approach relies on a fully polynomial time approximation scheme to solve the quadratic programming relaxation. This result is interesting in itself, because the underlying quadratic program is NP-hard to solve in general. We also briefly discuss variants of the problem and derive lower bounds.operations research and management science;
The Integration of Process Planning and Shop Floor Scheduling in Small Batch Part Manufacturing
In this paper we explore possibilities to cut manufacturing leadtimes and to improve delivery performance in a small batch part manufacturing shop by integrating process planning and shop floor scheduling. Using a set of initial process plans (one for each order in the shop), we exploit a resource decomposition procedure to determine schedules to determine schedules which minimize the maximum lateness, given these process plans. If the resulting schedule is still unsatisfactory, a critical path analysis is performed to select jobs as candidates for alternative process plans. In this way, an excellent due date performance can be achieved, with a minimum of process planning and scheduling effort
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