On the Stochastic and Asymptotic Improvement of First-Come First-Served and Nudge Scheduling

Recently it was shown that, contrary to expectations, the First-Come-First-Served (FCFS) scheduling algorithm can be stochastically improved upon by a called Nudge for light-tailed job size distributions. partitions jobs into 4 types based on their size, say small, medium, large and huge jobs. operates identical FCFS, except that whenever small arrives finds waiting at back of queue, swaps with one unless already involved in an earlier swap. In this paper, we show FCFS under far weaker conditions. We consider system 2 limited swapping between type-1 type-2 jobs, but where is not necessarily smaller than job. More specifically, introduce study Nudge- K which allows swapped up while most present explicit expression response time distribution when both follow phase-type distribution. Regarding asymptotic tail improvement ratio (ATIR), derive simple ATIR, as well maximizes ATIR. ATIR positive optimal tends infinity heavy traffic long are average longer