Resequencing delay for a queueing system with multiple servers under a threshold-type scheduling

The resequencing delay for a queueing system with multiple servers under threshold-type scheduling is analyzed. The general expressions for the average total delay, which is the sum of resequencing delay and queuing delay, are derived. The expressions are also applicable to the conventional M/M/n queuing system as the special case of zero-threshold policy. Next, the numerical calculation is carried out for a queuing system with three servers under a threshold-type schedule to consider the impact of the multiple thresholds on the average resequencing delay. It is found that the resequencing delay as well as the queuing delay for a queuing system with multiple servers of different service rates can be reduced under threshold-type scheduling by selecting the threshold values appropriately. Threshold-type scheduling is more effective in reducing the resequencing delay compared to the queuing delay, especially in the region of modest traffic intensity and as the difference in the service rates becomes larger