Gittin's index for job

When this job is put on the machine at time , then the discounted expected reward is given by .
When this job is put on the machine at time , then the discounted expected reward is given by .
When this job is put on the machine at time , then the discounted expected reward is given by .

Thus

Gittin's index for job

When this job is put on the machine at time , then the discounted expected reward is given by .
When this job is put on the machine at time , then the discounted expected reward is given by .
When this job is put on the machine at time , then the discounted expected reward is given by .

Thus

Gittin's index for job

When this job is put on the machine at time , then the discounted expected reward is given by .
When this job is put on the machine at time , then the discounted expected reward is given by .
When this job is put on the machine at time , then the discounted expected reward is given by .

Thus .

Thus considering the indices values of the jobs, out of ,  and ,  would be put on machine at time  and would be completed first. After the completion of job , we can take up either job  or job  as the Gittin's index for both the jobs are the same.