# Internal Backpressure for Onboard Crospoint-Buffered Switches with Port Multiplexing
## 5 Simulation and Evaluation
### Deterministic Scenario  
In the deterministic scenario, we use the ON-OFF model to simulate the burst traffic of overloaded ports and Bernoulli i.i.d arrival to simulate the traffic of non-overloaded ports. The positions of overloaded ports are fixed and the number of overload ports is eight. First, to illustrate how the BP mechanism works, let us analyze the evolution of the queue length. In this simulation, input port 1 is the overload port and input port 2 is the non-overload port. Input port 1 and input port 2 are in the same SIM and therefore require the output to be forwarded through the same CQ. As shown in Figure 5(a), input port 1 is an overloaded port, and the queue length increases rapidly and reaches a stable state, indicating that the queue is full. However, due to the aforementioned HOL phenomenon,  
Figure 5: (**a**) State transition diagram of ON–OFF model. (**b**) Non-uniform traffic distribution model. input port 2, a non-overloaded port, experiences an unexpected surge in its queue length, leading to an overloaded state. Figure 6b delves into the impact of implementing BP mechanisms on queue lengths. Prior to the adoption of BP, it is evident that the accumulation of data processing pressure was gradual and significant. Subsequent to introducing the BP mechanism, a notable reduction is observed in the number of data buffers at both input and output ports. This underscores the effectiveness of the BP mechanism in alleviating the pressure within the data traffic. Next, the effects of \(\omega\) on switching network performance under different BP mechanisms are analyzed. In this simulation, we use an ON-OFF model to simulate burst traffic, where the average length of the on state is 1200 and the average length of the off state is 800. The \(\omega\) ranges from 0.4 to 0.5, indicating that the degree of the traffic imbalance is of a moderate value. We consider the case without BP as a comparison, which is denoted as no-BP. When analyzing the influence of imbalance factor \(\omega\) on system performance under different BP mechanisms, we first analyze the influence of \(\omega\) on packet delay under different BP mechanisms. It can be found that under the _det_non_ traffic model, with the increase in \(\omega\), the packet delay shows an increasing trend. As shown in Figure 7a, according to the simulation results, the packet delay of BP load balance, BP fine and BP load detection mechanisms is only increased by about 3.1-4.1% compared to the no-BP structure. Secondly, we analyze the influence of \(\omega\) on the packet loss rate under different BP mechanisms. Figure 7b shows that an increase in imbalance factor \(\omega\) will lead to an increase in the packet loss rate. However, after the introduction of the BP mechanism, especially for the BP load balance mechanism, the packet loss rate is significantly reduced compared to that of the no-BP mechanism. Under the deterministic scenario, when \(\omega\) reaches 0.5, compared with no-BP, the packet loss rate corresponding to the added BP load balance is reduced by 12%, which shows the best effect when dealing with non-uniformity traffic. The performance of BP fine and BP load detection is similar, and the packet loss rate is about 4.1% and 8.2% lower than that of the no-BP scheme, respectively. Finally, we analyze the effects of \(\omega\) on throughput under different BP mechanisms. In Figure 7c, it can be found that under the deterministic scenario, with an increase in \(\omega\), the overall throughput of the system will show a downward trend. When evaluating the effects of different BP mechanisms, the BP load balance mechanism shows better performance in dealing with a non-uniform traffic distribution; that is, when \(\omega\) is 0.5, its  
Figure 6: (**a**) The relationship between queue length distribution and time without BP. (**b**) The relationship between queue length and time under the BP mechanism. corresponding throughput rate can reach about 79.8%.