The Mitrani-King-Nishida (MK-N) approximation

The MK-N approximation analyzes the mean delay of class $i$ jobs in an M/M/$k$ queue with $m\geq 2$ priority classes by aggregating all the higher priority classes (classes 1 to $i-1$). The job size distribution of the aggregated class is then approximated with an exponential distribution by matching the first moment of the distribution.

In MK-N, the job size distribution of the aggregated higher priority classes is approximated by an exponential distribution, since the exact or nearly exact analysis of a multiserver system with two priority classes are known only for exponential distributions. However, DR that we have developed in Chapter 2 allows us to analyze the multiserver system with two priority classes for the case where job sizes have PH distributions, and the moment matching algorithm that we have developed in Chapter 2 allows us to approximate the job size distribution of the aggregated higher priority classes by a PH distribution matching the first three moments. This motivates us to extend the MK-N approximation to PH distributions: DR-A.