# New RED-Type TCP-AQM Algorithms Based on Beta Distribution Drop Functions
## 3 Scenarios of Simulation and Metrics
### Performance Metrics  
The ultimate goal of TCP/AQM protocols is to improve the performance of end-user metrics. However, the final performance is strongly influenced by the performance of router-based metrics. Thus, to evaluate the performance of the proposed algorithms, we have chosen to use two router-based metrics and three end-user metrics. The following is a brief description of the most important characteristics of the metrics used for performance evaluation:  
Figure 1: Network topology.  
* Average queue length (AQL). The queue size indicates the number of packets pending transmission in the buffer queue. An unstable system is usually characterized by a synchronization in the TCP queues, accompanied by strong oscillations. Under suitable settings, the average queue length tends to stabilize at a value that we refer to as the equilibrium point. One of the main objectives of AQM algorithms is to stabilize the buffer queue size and, in this sense, we shall refer to the stability of an AQM algorithm as the ability to maintain the average queue length (or the average queuing delay) around a certain target value. The stability is an important performance characteristic of TCP/IP networks.
* The packet drop rate. It measures the ratio of the number of packets dropped by an AQM to the total number of packets in queue. In this count, packets dropped by the link or channel at the physical layer are not counted, considering only the drop rate at the network layer. The main objective of an AQM is to maintain a stable queue size with as low packet drop rate as possible. This increases the performance, since dropped packets are an early signal of congestion to the TCP, causing a decrease in its send rate.
* End-to-end throughput. This is a performance measure obtained between two interlocutors (server-host). It measures the actual transmission of the total data propagated with respect to the simulation time (from the time the data is sent to the time it is received). It is defined as the number of bits received correctly per unit of time. Specifically, the calculation of this metric is obtained from the ratio between the number of bits received by the server/host and the time elapsed between the reception of the first segment and the last one. To calculate the throughput in the dumbbell type topology, we have averaged the ratio between the number of bits received by the left and right hosts, and the sum of elapsed time between the reception of the first segment and the last one at each of these nodes.
* End-to-end delay (latency). It is one of the most significant metrics in a communication system and, in general terms, it is the time required to transmit a segment along its entire length, end-to-end. Specifically, it is calculated using the equation: \[\text{Latency}=\text{propagation time}+\text{transmission time}+\text{ queuing time}+\text{processing delay}\] For its calculation in the dumbbell topology, the end-to-end delay times of all the segments sent between the left and right hosts are summed, divided by the number of segments received on both hosts.
* Jitter. Jitter in a flow is defined as the variation in delay of arriving packets over time. A very high jitter can cause packet loss due to buffer overflow. In the dumbbell topology, an average value is calculated by summing the time variations between the correlative packets of all flows, and dividing by the number of variations.  
All simulations presented in this paper were performed with ns-3 [37]. This is a discrete event network simulator for Internet systems, primarily intended for research and educational use. It is free software, licensed under GNU GPLv2, and is publicly available for research, development and use.