Amortized efficiency of list update and paging rules
Communications of the ACM
On the competitiveness of on-line real-time task scheduling
Real-Time Systems
Memory versus randomization in on-line algorithms
IBM Journal of Research and Development
Efficient on-line call control algorithms
Journal of Algorithms
Scheduling for Overload in Real-Time Systems
IEEE Transactions on Computers
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Competitive non-preemptive call control
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Online scheduling with hard deadlines
Journal of Algorithms
Speed is as powerful as clairvoyance
Journal of the ACM (JACM)
Bandwidth Allocation with Preemption
SIAM Journal on Computing
Real-Time Systems: Design Principles for Distributed Embedded Applications
Real-Time Systems: Design Principles for Distributed Embedded Applications
Competitive routing of virtual circuits in ATM networks
IEEE Journal on Selected Areas in Communications
Admission control with immediate notification
Journal of Scheduling - Special issue: On-line scheduling
Gradual Relaxation Techniques with Applications to Behavioral Synthesis
Proceedings of the 2003 IEEE/ACM international conference on Computer-aided design
Competitive analysis of most-request-first for scheduling broadcasts with start-up delay
Theoretical Computer Science
An Optimal Strategy for Online Non-uniform Length Order Scheduling
AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
Online nonpreemptive scheduling of equal-length jobs on two identical machines
ACM Transactions on Algorithms (TALG)
On Job Scheduling with Preemption Penalties
AAIM '09 Proceedings of the 5th International Conference on Algorithmic Aspects in Information and Management
Improved upper bounds on the competitive ratio for online realtime scheduling
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Online deadline scheduling with preemption penalties
Computers and Industrial Engineering
Online, non-preemptive scheduling of equal-length jobs on two identical machines
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Maximizing the throughput of multiple machines on-line
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
Laxity helps in broadcast scheduling
ICTCS'05 Proceedings of the 9th Italian conference on Theoretical Computer Science
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We consider the online competitiveness for scheduling a single resource non-preemptively in order to maximize its utilization. Our work examines this model when parameterizing an instance by a new value which we term the patience. This parameter measures each job's willingness to endure a delay before starting, relative to this same job's processing time. Specifically, the slack of a job is defined as the gap between its release time and the last possible time at which it may be started while still meeting its deadline. We say that a problem instance has patience κ, if each job with length ||J|| has a slack of at least κ ċ ||J||.Without any restrictions placed on the job characteristics, previous lower bounds show that no algorithm, deterministic or randomized, can guarantee a constant bound on the competitiveness of a resulting schedule. Previous researchers have analyzed a problem instance by parameterizing based on the ratio between the longest job's processing time and the shortest job's processing time. Our main contribution is to provide a fine-grained analysis of the problem when simultaneously parameterized by patience and the range of job lengths. We are able to give tight or almost tight bounds on the deterministic competitiveness for all parameter combinations.If viewing the analysis of each parameter individually, our evidence suggests that parameterizing solely on patience provides a richer analysis than parameterizing solely on the ratio of the job lengths. For example, in the special case where all jobs have the same length, we generalize a previous bound of 2 for the deterministic competitiveness with arbitrary slacks, showing that the competitiveness for any κ ≥ 0 is exactly 1 + 1/(⌊κ⌋ + 1). Without any bound on the job lengths, a simple greedy algorithm is (2+ 1/κ)- competitive for any κ 0. More generally we will find that for any fixed ratio of job lengths, the competitiveness of the problem tends towards 1 as the patience is increased. The converse is not true, as for any fixed κ 0 we find that the competitiveness is bounded away from 1, no matter what further restrictions are placed on the ratio of job lengths.