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## Comparing DR-A with BB and MK-N

Figure 4.7: Comparison of DR-A, MK-N, and BB approximations for M/PH/2 with 4 priority classes with , , , and , as a function of . Here, the squared coefficient of variability of the job size distributions are (top two rows) or (bottom two rows) for all classes. Load is balanced among the classes. Note that MK-N does not appear for , because the error is beyond the scale of the graphs for most values of .
Comparison of approximations for M/M/2 with 4 priority classes ()
 (a) Class 2
 (b) Class 3
 (c) Class 4
Comparison of approximations for M/PH/2 with 4 priority classes ()
 (a) Class 2
 (b) Class 3
 (c) Class 4

We now evaluate the accuracy of DR-A, BB, and MK-N. In all figures, we assume servers and priority classes. We consider both the case where each priority class has an exponential job size distribution (; top half of Figure 4.7) and the case of two-phase PH job size distributions with (bottom half of Figure 4.7)4.3. Each class may have a different mean job size, and these are chosen to vary over a large range, determined by parameter . Specifically, the mean job size of class is set , where . Thus, implies small high priority jobs. We equalize the load between the classes, i.e. , where is the load of class . With these settings, the error in mean delay is evaluated for each class of jobs, where the error of an approximation is defined as follows:

Thus, positive error means overestimation and negative error means underestimation of the approximation. Simulation is kept running until the simulation error becomes less than 1% with probability 0.95 (see Section 3.9 for more technical details of our simulation).

In evaluating the BB and MK-N approximations, we use accurate methods known to compute their components. For example, BB relies on knowing the mean delay for the M/PH//FCFS queue. We compute this delay precisely for the PH job size distribution using matrix analytic methods. MK-N relies on being able to analyze the case of two priority classes (since classes are reduced to two). We analyze the two priority class case in MK-N using DR. We first discuss the accuracy of MK-N and DR-A, and then discuss the accuracy of BB.

Subsections

Next: The MK-N and DR-A Up: New approximations for many Previous: New approximation: DR-A   Contents
Takayuki Osogami 2005-07-19