SIMULATION RESULTS | Capacity Planning and Design

The average-based design models lead us to much smaller estimates of required capacity. Therefore, they run the risk of not being able to guarantee acceptable performance for many real-time applications such as voice or video where jitter must also be taken into account. We currently do not have design models that can take jitter into account so we need to evaluate whether the jitter remains acceptable in a system designed with an average delay method.

In this section, we present simulation results to study the delays encountered by the individual voice and video sources under various provisioning scenarios and compare them with the required delays for voice and video, respectively. We used ns-2 to conduct simulations. In this section, we only consider AF subclasses where multiple sources send packets to each subclass, and packets of each subclass are served in the order of their arrival while sharing bandwidth between the subclasses using PDD scheduling. The simulation model for AF class is shown in Figure 1. We simulate a voice source using a two state on–off model where it generates packets with a deterministic inter-arrival time of 15 ms in the on-state. On-periods are exponential with rate 2.5 and off-periods are also exponential with a rate 1.67. Each packet is of size 120 bytes. The video source is modeled using deterministic batch arrivals with batch inter-arrival time of 33 ms. The number of packets in a batch are geometrically distributed with an average of five packets. In each burst, the last packet has size distributed as uniform (0,1000) bytes. All other packets have 1000 bytes.

 
Figure 1: Simulation model for AF class.

Here also c_LB/r, c_OO/r, and c_P/r refer to overprovisioning required when, dimensioning for average delays using LB based model, using on–off-based model and Poisson-based model, respectively. Observe that the capacity computed using these models along with PDD-based scheduling for single, five, and ten voice and video sources. Now we use that capacity for the simulation and compare in Figures 2 through 7 the delays for single, five, and ten voice and video sources. We have plotted the observed mean delay and error bars corresponding to twice the sample standard deviation for voice and video sources. We also present a horizontal line showing the required average delay for each source.

 
Figure 2: Delay for single voice source.

 
Figure 3: Delay for single video source.

 
Figure 4: Delay for five voice source.

 
Figure 5: Delay for five video source.

 
Figure 5: Delay for ten voice source.

 
Figure 6: Delay for ten video source.

Note that for the Poisson-based capacity model with single sources, the actual mean delay is many times the target delay, both for voice and video. Moreover, some voice packets can have a delay as high as 400 ms and will be useless at the receiver. For video also, packets can have delays as much as 1 s. Such a capacity planning is not very useful and could lead to unsatisfied customers. When we multiplex five or ten voice and video sources, the average delays get closer to the target delays and for ten sources, they are even acceptable for both voice and video. However, there is still a large variance in the observed delays and voice packets could still have as high as 40 ms and video as high as 100 ms. Note that such high delays could be tolerable if they affect only a small number of packets.

Next, we consider on–off and LB-based design models. Observe that both the approaches provide acceptable delays, average as well as average along with two times standard deviation. The values are smaller than the required delays and hence a significant fraction of packets belonging to voice and video sources will encounter less than required delays. These models remain consistent for single, five, or ten sources and provide acceptable, performance to individual sources. Note that the LB-based model provides delays which are less than the target for both voice and video, although it requires lesser capacity than the on–off-based models. Observe that not only the delays are acceptable but also the variance is quite small.

Based on these results, it can be argued that LB-based model could be used to determine required capacity for a source requesting an average delay QoS. When allocating capacity for a small number of sources, it can achieve the multiplexing gain and provides minimal capacity to meet the required delays.