In this paper, the authors propose two parallel M/M/1 queueing systems with dynamic routing under a threshold-type scheduling. Arriving customer is sent to the buffer of the faster server as far as the difference of two queues does not exceed a threshold value, but it 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 as the difference of the two service rates becomes large, the two parallel M/M/1 queueing systems with dynamic routing under the threshold-type scheduling can reduce the mean queueing time of customers in the system compared to the conventional nonthreshold-type one. It is also found that as the asymmetry in the two service rates increases, the optimum threshold value which minimizes the mean queueing time should be large to reduce the number of queueing customer in the buffer of the slower server. On the other hand, as the traffic intensity becomes large, the optimum threshold value tends to be small in order to increase the total service rate.
