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Online scheduling in identical machines with makespan minimization has been awell studied research problem in the literature. In online scheduling, thescheduler receives a list of jobs one by one and assigns each incoming job onthe fly irrevocably to one of the machines before the arrival of the next job.In this paper, we study a variant of the online scheduling problem, where jobsare requested on the fly from k distinct sources. On simultaneous arrival ofjobs from multiple sources, it is a non-trivial research challenge to ensurefairness in scheduling with respect to distinct sources, while optimizing theoverall makespan of the schedule. We develop a novel Multi Lists SchedulingModel(MLS) and propose a 2-competitive deterministic online algorithm namelyLargest Job on Least Loaded Machine(LJLLM) based on the MLS model to addressthe above mentioned research challenge.

A 2-Competitive Largest Job on Least Loaded Machine Online Algorithm based on Multi Lists Scheduling Model