Alternating priority versus FCFS scheduling in a two-class queueing system

For the single-server two-class queueing system studied in the classical text of Conway et al. (1967) [2], we compare the mean flow times for First-Come, First-Served (FCFS) and Alternating Priority (AP) scheduling rules assuming zero setup costs for switching between classes. We show that the condition for the superiority of AP over FCFS stated in that text is incorrect, provide the correct conditions, and establish a lower bound on the difference between the mean flow times under the two rules.