Analysis of queueing systems with multiple servers under a threshold-type scheduling

The queueing system with multiple servers of possible different rates under a threshold-type scheduling is analyzed. The authors first derive the general expressions for state probabilities and the average queueing delay in which the conventional M/M/n queueing system is also included as the special case of zero-threshold policy. Next, the numerical calculation is carried out for the queueing system with 3 servers under a threshold-type scheduling to consider the impact of the multiple thresholds on the average queueing delay of the system. It is found that the average queueing delay of the queueing system with multiple servers of different rates can be reduced under a threshold-type scheduling by selecting the threshold values appropriately. The threshold-type scheduling is more effective as the difference of the service rates becomes larger.