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

A queuing system with multiple servers of different rates under a threshold-type scheduling is analyzed. The authors derive the general expressions for state probabilities and the average queuing delay in which the conventional M/M/n queuing is also included as the special case of the zero-threshold policy. A numerical calculation is carried out for a queuing system with three servers under threshold-type scheduling in order to consider the impact of the multiple thresholds on the average queuing delay of the system. It is found that the average queuing delay of the queuing system with multiple servers of different rates can be reduced under threshold-type scheduling by selecting the threshold values appropriately. Threshold-type scheduling is more effective as the difference between the service rates becomes larger. It is also shown that computer simulation results agree well with the theoretical results.>