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Consider a discrete time slotted, system with two categories of jobs $J_1$ and $J_2$, where each job from the category $J_1$ has completion time requirement of $C_1$ and the jobs from category $J_2$ do not have any completion time requirement. The system can process jobs concurrently wherein the completion time of $k$ jobs executing concurrently is $\tau$ per slot, determined by a linear function of the number of jobs currently in the system (independent of job category). For a particular arrival rate of $R_1$ per slot for jobs of category $J_1$, and arrival rate per slot of $R_2$ for jobs of category $J_2$, determine the number of jobs of each category to process in each slot so as to ensure that all jobs in $J_1$ adhere to the completion time requirement. It is known apriori that $R_1 - \epsilon = k$, for a fixed $\epsilon$, thereby ensuring that jobs from $J_2$ could indeed be executed concurrently . Would a linear programming solution be feasible in this case? If the completion time function is non-linear what would be a feasible approach then?

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  • $\begingroup$ Would you please, give a simple example of what you are looking for? $\endgroup$
    – A.Omidi
    May 14 at 8:48

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