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1. E. Hyytiä and R. Righter, Fairness Through Linearly Increasing Holding Costs in Systems of Parallel Servers with Setup Delays, in 27th International Teletraffic Congress (ITC'27), 2015, Ghent, Belgium (bib)

   Abstract: 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. However, longer waiting time is likely to increase the ``anxiety level'' of a customer. We take fairness into account by defining a linearly increasing holding cost model, where the holding cost of job i is defined by two non-negative random variables, that could depend on the service time, giving the instantaneous holding cost rate. 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 techniques. The policies are finally evaluated numerically.