Validation

- DR has a very small error in predicting the first order metric such
as mean delay and mean queue length. Specifically, the error in DR
is within 3% for a range of parameters (loads, service demand distributions,
and the number of classes, ) in the analysis of both
the preemptive priority queue and
`SBCS-ID`. - The error in DR is slightly larger but is still small in predicting
the second order metric such as the second moment of the queue length.
Specifically, the error is within 7% for a range of parameters
in the analysis of
`SBCS-ID`. - The error in DR-PI and DP-CI is slightly larger than DR but is still small
for both the first and second order metrics. Specifically, the error
is within 6% (respectively, 10%) in predicting the first (respectively, second)
order metric for a range of parameters in the analysis of
`SBCS-ID`. - DR is computationally quite efficient when it is applied to 2D Markov chains, i.e. RFB processes with (FB processes) and GFB processes. Specifically, in the analysis of the preemptive priority queue, the running time of DR is seconds for up to servers.
- The running time of DR can grow quickly as the number of processes,
, in an RFB process increases. Specifically, in the analysis
of the preemptive priority queue with servers,
the running time of DR is within 30 seconds for up to
classes (processes); however, in the analysis of
`SBCS-ID`, DR becomes computationally prohibitive with classes (processes). - DR-PI and DR-CI can reduce the running time of DR significantly.
Specifically, in the analysis of
`SBCS-ID`, the running time of DR-CI is within 30 seconds for up to classes (processes).