Scheduling Periodic Jobs that Allow Imprecise Results
IEEE Transactions on Computers
Minimizing service and operation costs of periodic scheduling
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Scheduling Algorithms for Multiprogramming in a Hard-Real-Time Environment
Journal of the ACM (JACM)
Windows scheduling problems for broadcast systems
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Pfair Scheduling of Generalized Pinwheel Task Systems
IEEE Transactions on Computers
Periodic Scheduling with Service Constraints
Operations Research
Optimal Reward-Based Scheduling of Periodic Real-Time Tasks
RTSS '99 Proceedings of the 20th IEEE Real-Time Systems Symposium
Windows scheduling as a restricted version of Bin Packing
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
A general buffer scheme for the windows scheduling problem
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
A general buffer scheme for the windows scheduling problem
Journal of Experimental Algorithmics (JEA)
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We consider a problem of repeatedly scheduling n jobs on m parallel machines. Each job is associated with a profit, gained each time the job is completed, and the goal is to maximize the average profit per time unit. Once the processing of a job is completed, it goes on vacation and returns to the system, ready to be processed again, only after its vacation is over. This problem has many applications, in production planning, machine maintenance, media-on-demand and databases query processing, among others. We show that the problem is NP-hard already for jobs with unit processing times and unit profits, and develop approximation algorithms, as well as optimal algorithms for certain subclasses of instances. In particular, we show that a preemptive greedy algorithm achieves a ratio of 2 to the optimal for instances with arbitrary processing times and arbitrary profits. For the special case of unit processing times, we present a 1.67-approximation algorithm for instances with arbitrary profits, and a 1.39-approximation algorithm for instances where all jobs have the same (unit) profits. For the latter case, we also show that when the load generated by an instance is sufficiently large (in terms of n and m), any algorithm that uses no intended idle times yields an optimal schedule.