Two parallel queues with dynamic routing under a threshold-type scheduling

摘要

The authors propose two parallel M/M/1 queuing systems with dynamic routing under threshold-type scheduling. An arriving customer is sent to the buffer of the fast server as long as the difference of two queues does not exceed a threshold value: the customer should be sent to the buffer of the slower server if and only if the difference of two queues exceeds a threshold value. It is shown that the two parallel M/M/1 queuing systems under threshold-type scheduling can reduce the mean queuing time compared to conventional parallel M/M/1 queuing systems not using the threshold-type policy, and that the mean queuing time is minimized by selecting the threshold value appropriately.