DR-CI (DR with complete independence assumption) ignores not only the dependency that the length of the sojourn time in levels has on how the Markov chain enters levels but also the dependency on how it exits from levels (to level ). Specifically, we assume that is independent of and . Let for all and , and let denote the process that is the same as except that is replaced by for all and . Figure 3.27(b) shows the Markov chain for the high priority jobs (background process) that is obtained via DR-CI in the analysis of an M/PH/2 queue with two priority classes. In DR-CI, the four types of busy periods are represented by a single PH distribution, ignoring the dependency that the duration of the busy period has on the phase of the job in service at the beginning and end of the busy period.
We choose such that has the above two key properties that has. The difference between and lies in the dependencies in the sequence of the sojourn times in levels . Observe that the sequence of the sojourn times in levels is i.i.d. in , while it has some dependencies in .
More formally, the generator matrix
, is determined as follows.
Let be the -th moment of for .
We determine so that
the same marginal -th moment of the sojourn time in levels :