  Online scheduling in identical machines with makespan minimization has been a
well studied research problem in the literature. In online scheduling, the
scheduler receives a list of jobs one by one and assigns each incoming job on
the 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 jobs
are requested on the fly from k distinct sources. On simultaneous arrival of
jobs from multiple sources, it is a non-trivial research challenge to ensure
fairness in scheduling with respect to distinct sources, while optimizing the
overall makespan of the schedule. We develop a novel Multi Lists Scheduling
Model(MLS) and propose a 2-competitive deterministic online algorithm namely
Largest Job on Least Loaded Machine(LJLLM) based on the MLS model to address
the above mentioned research challenge.
