# Internal Backpressure for Onboard Crospoint-Buffered Switches with Port Multiplexing
## 5 Simulation and Evaluation
### Stochastic Scenario  
In the stochastic scenario, each output port has two types of traffic: background traffic and burst traffic. We use Bernoulli i.i.d arrival to simulate background traffic and the ON-OFF model to simulate burst traffic. The background traffic is evenly distributed across each output port. The burst traffic is concentrated in traffic hot ports. The locations of hot ports are randomly distributed, with an average number of eight. First, the effect of burst length on performance in the ON-OFF model is analyzed. In this experiment, the average length of our fixed off state is 800 time slots. We consider the case without BP as a comparison, which is denoted as no-BP. In Figure 8a, it can be found that the packet delay gradually increases with an increase in burst length, and the packet delay under different BP mechanisms is slightly higher than that under no-BP schemes. This is because the balance adjustment process after the addition of the BP mechanism is not instantaneous but requires a certain amount of time and computing resources. During the BP mechanism, the upstream data processing node may pause or slow down the transmission of data, waiting for the downstream processing node to have sufficient capacity to process the new data. This can lead to an increase in the amount of time packets waiting in the processing queue, which increases packet delay. In addition,  
Figure 7: (**a**) The influence of \(\omega\) on the packet delay of each BP mechanism under the deterministic scenario. (**b**) The influence of \(\omega\) on the packet loss rate of each BP mechanism under the deterministic scenario. (**c**) The influence of \(\omega\) on the throughput of each BP mechanism under the deterministic scenario model. the BP mechanism may also trigger a series of chain reactions. When a node triggers BP, its upstream nodes may also be affected, resulting in a decrease in the rate of the entire data processing process. In this case, packet delays can accumulate throughout the process, making the final delay more noticeable. Therefore, the BP mechanism should be designed with the packet delay as small as possible. The results show that when the burst length reaches 1500, the packet delay of BP load balance and BP fine is similar, only increasing by 3.7%. Secondly, we analyze the effect of burst length on the packet loss rate under different BP mechanisms. As shown in Figure 8b, the packet loss rate increases with the increase in burst length. This is because when the buffer is about to be fully loaded, the BP mechanism can adjust the upstream send rate in time, in fact, to provide more processing time for the downstream processing node, so as to avoid packet loss caused by buffer overflow. The actual results show that under the same burst length, the BP load balance mechanism has the lowest packet loss rate. When the burst length reaches 1500, the packet loss rate is reduced by about 12% compared to the scheme without BP. The packet loss rates of BP fine and BP load detection were reduced by 2.8% and 5.8%, respectively. Finally, we analyze the effect of burst length on throughput under different BP schemes. As shown in Figure 8c, the higher the burst length, the lower the throughput of the system. This is because the high burst length means that there is a large amount of data in a short time, resulting in the fact that the processing unit cannot process data in a timely manner, thus reducing the overall processing capacity of the system. When comparing different mechanisms, we can see that the performance of the BP load balance mechanism is the best, and the throughput rate can reach more than 76% when the burst length is 1500. This mechanism can deal with burst data better and maintain high throughput through its effective load balancing strategy. In contrast, the no-BP mechanism slightly underperformed.