Analysis of a multistage queue

Multistage queueing mechanisms with quantum service are suitable in various computer and communication systems to guarantee small delays to short jobs without first knowing the service requirement of any job. In this paper we analyze the efficacy of one such scheme — a two-stage First-In First-Out (FIFO) and Round Robin (RR) — in discriminating between short and long jobs. We obtain the distribution of the delay for short jobs, the cycle time in the RR queue for long jobs, and the number of messages in the FIFO and the RR queues. For the specific parameters used in our numerical results, the two-queue scheme seems to discriminate effectively between the long and short jobs.