Introduction of “Additional” Traffic

α

Figure 4-5. Allowable Mean from 20 Queue Scenario

The results shown in Figure 4-3 and the results of comparing Figure 4-4 and Figure 4-5 show that the allowable mean developed through the technique proposed here is an effective means of estimating the true mean number of empty timeslots per WRR cycle. The estimate rapidly converges to the true mean when existing traffic has short burst characteristics, taking longer to converge when the existing traffic has long burst characteristics. Thus, as the number of served queues increases,

improvements in the time of convergence results.

4.1.5 Introduction of “Additional” Traffic

In order for the proposed method of connection admittance to be effective, traffic at rates determined from the multiple and single empty timeslot methods of Chapter 3 must be supported by the virtual path for each value of µ_X, the mean number of

empty timeslots per cycle. To determine if this is the case, the path model of a “full”

virtual path is modified by the addition of a traffic stream and queue having definable traffic parameters and queue size parameters. To insure validity across the range of possible mean values and the corresponding “added” connection sustainable cell rates, the fixed probability scenarios listed in Appendix B2 were used.

Since the queue sizes associated with the “added” connections, as discussed in Section 3.4.3, are based on a worst case analysis, the initial simulations were run first with “added” queue lengths of MQL, as determined by Equation (3.5), rather than the augmented queue lengths, MQL’, specified in Section 3.4.3. This allows for the development of a baseline where there are no augmented “added” queue sizes for use in future evaluations of the need for specific “added” queue sizes larger than MQL. It also allows the total number of required simulations to be reduced, since the results of initial simulations will indicate areas of mean and burst size parameters where

additional simulation are actually needed.

Simulations were run such that within each “existing” traffic scenario, taken from Appendix B2, having various SCR and short, mixed, or long burst size characteristics,

“added” traffic was introduced through a queue sized at either MQL or MQL’, as discussed above. Simulations were run 20 times each, using a different random seed, for each “added” traffic characteristic type within each SCR tested. The “added”

traffic characteristic types used mean burst characteristics of 2, 10, and 100 for each set of parameters within the empty queue probability parameters of .1, .5, and .9

shown in Appendix B2. The simulations were run such that the “added” traffic SCR was greater than the predicted allowable “added” traffic SCR, and was increased on successive runs until the allowed CLR (10^-3 in this case) was exceeded. In cases where the CLR was exceeded at the first value tested, the SCR was reduced on successive simulation runs until the CLR was below that required, or until the SCR was below the allowable “added” SCR for that “existing” traffic scenario. A CLR threshold was defined such that it existed at the boundary between two added traffic SCR values, the higher value being where the CLR was exceeded, and the lower one where the CLR was not exceeded. A typical graph resulting from this procedure is shown at Figure 4-6, with detailed results being shown in Appendices C, D, and E.

Results of initial simulations of 10 queue, 10 timeslot fixed probability scenarios 1, 2, and 3, for short, mixed, and long burst existing traffic types taken from

Appendix B2 are shown in Appendix C, Figures C-1 through C-9. The results show the cell loss ratios were better than required for all “existing” traffic scenarios and burst types other than Scenario 2, where the normalized mean number of empty timeslots per cycle is .1, with existing traffic having long burst characteristics, as seen in Figure C-6. This characteristic, where CLR did not meet requirements for low mean, long burst existing traffic scenarios, was apparent in other scenario sequences, as well. This is illustrated by Scenario 5, Figures C-10 through C-12, where the long burst scenario causes excessive CLR at additional traffic rates that should be

acceptable, as seen in Figure C-12. This was also true in the case of Scenario 8, long burst existing traffic, as illustrated by Figure C-13.

4 Evaluation and Discussion of Res 10 Queue, 10 Timeslot Fixed Utilization Scenario 1 (Short Bursts) CLR of Added Traffic using Normal Max Queue Lengths 0.00010.0010.01

0.1

1 1sh- 1a1sh- 1c1sh- 1e1sh- 2a1sh- 2c1sh- 2e1sh- 2f1sh- 2h1sh- 2j1sh- 3a1sh- 3c1sh- 3e1sh- 3f1sh- 3h1sh- 3j1sh- 3k1sh- 3m1sh- 3o1sh- 4a1sh- 4c1sh- 4e1sh- 4f1sh- 4h1sh- 4j1sh- 4k1sh- 4m1sh- 4o1sh- 5a1sh- 5c1sh- 5e1sh- 5f1sh- 5h1sh- 5j1sh- 5k1sh- 5m1sh- 5o1sh- 5p1sh- 5r1sh- 5t1sh- 6a1sh- 6c1sh- 6e1sh- 6f1sh- 6h1sh- 6j1sh- 6k1sh- 6m1s 6o Added Traffic Rate (Normalized to Rvp) [Various Utilizations and Burst Sizes]

CLR

MAX Allowable Traffic Rate = .113Rvp (Multiple Empty Timeslot Method )

Allowable CLR = .001 CLR Threshold Rate = .4Rvp .1 .2 .3 .4 .5 .6

(of 20 random tria

Normalized Mean = .5 Allowable Traffic Rate = .067Rvp (Single Empty Timeslot Method ) [Off Chart] Figure 4-6. Typical “Added” Queue Simulation Results 4-21

The initial simulation runs described above achieved their objective of

determining the traffic characteristics that would cause “additional” traffic connection queue overflows in queues sized by Equation 3.5, thus indicating which scenarios should be run with the augmented “added” queue lengths required by Equation (3.25).

Scenarios 2, 5, and 8 were then run with the augmented “added” queue lengths required by section 3.4.3, with the results shown in Appendix D, Figures D-1 through D-3. As illustrated in these figures, all results of simulations using augmented

“added” queues met the required CLR.

To further evaluate the model, 20-queue models were tested, using the scenarios shown in Appendix B3. Results from 20-queue, 20-timeslot Scenario 2, for short, mixed, and long existing traffic burst characteristics are shown at Appendix E, Figures E-1 through E-3. All 20-queue models tested met the required CLR without the need for augmented queues on “added” traffic connections. The implication of the results obtained above will be discussed in the next section.