Approximations of the mean resequencing waiting time in M/GI/c systems

The problem of obtaining approximate formulas for mean resequencing waiting times of M/GI/c queueing systems is considered. Two assumptions, commonly used in the study of M/GI/c systems, to derive the formulas are adopted. The formulas are quite accurate and the accuracy increases as c becomes larger. The relative differences between simulation results and the ones calculated by the formulas are below 4%, even for larger server utilization (ρ). For small ρ, the differences are below 1%. Both small ρ, the differences are below 1%. Both numerical and simulation results indicate that when the squared coefficient of variation of service time distribution is greater than 1, the mean resequencing waiting time is likely to be very large