Waiting time in a combined first-come-first-served and shortest-time-first queue

In this paper, we study the regular M/G/1 queue with a combination of FCFS and STF queueing disciplines. The advantage of this combined discipline is the reduction of mean waiting time. Customers are divided into two groups: an FCFS group and an STF group. Customers are first put into FCFS group and are then moved into STF group. An embedded Markov chain is formulated at the times when the STF group is empty. Results are compared with regular M/G/1 queues of FCFS.