Fairness through Linearly Increasing Holding Costs in Systems of Parallel Servers with Setup Delays

We consider a system of parallel servers, where arriving jobs are routed to one of the servers upon arrival. The standard objective of minimizing the mean sojourn time (delay) does not enforce any kind of fairness in the system and it is acceptable, e.g., to delay one job a lot if it reduces the sojourn time of some other jobs. We take fairness into account by defining a linearly increasing instantaneous holding cost rate by two job-specific non-negative random variables, (ai; ßi), that can depend on the service time. We focus on first-come-first-served (FCFS) and preemptive last-come-first-served (LCFS) scheduling, and derive the so-called value functions for the corresponding M/G/1 queues. Then we apply these results and obtain cost aware dispatching policies by means of policy improvement and lookahead. The policies are finally evaluated numerically.