在 TCP Tahoe 中找到最终的拥塞窗口大小

给定初始拥塞窗口大小cwnd 、阈值ssthresh 、连接时间rtt和数组arr ，其中 arr[i] 表示检测到丢包的时间。任务是在发送方遇到所有丢包时找到最终的拥塞窗口大小。

The TCP Tahoe follows below conditions:

• The initial value of cwnd is 10.
• Before reaching ssthresh, double cwnd per unit of time. By doubling the value, cwnd can’t cross ssthresh value, it can almost go up to ssthresh value.
• After reaching ssthresh, increase cwnd by 1 per unit of time.
• When there is packet loss, reduce the ssthresh to half of cwnd value (50%), reset cwnd to initial value of 10 and no other updation happens.
• The connection will be active until rtt unit of time.

例子：

Input arr[] = {16, 25}, ssthresh = 320, rtt = 28
Output: 80
Explanation:
Time = 0: cwnd = 10
Time = 1: cwnd = 20
Time = 2, 3, 4, 5: cwnd = 40, 80, 160, 320
cwnd=ssthresh at time=5, so now onwards cwnd increases by 1 per unit of time.
Time = 6-15: cwnd = 321-330
Time = 16: packet loss is detected, so ssthresh will become half of current cwnd value.
ssthresh = 330/2=165, cwnd = 10 (reseted), Note: cwnd is not increased by 1 or doubled in this case. 
Time = 17, cwnd = 20
Time = 18, cwnd = 40
Time = 19, cwnd = 80
Time = 20, cwnd = 160
Time = 21, cwnd = 165 {cwnd can’t get doubled because 320>165, it will cross the ssthresh. It can go max upto ssthresh}
Time = 22, cwnd = 166,  so now onwards cwnd increases by 1 per unit of time.
Time = 23, cwnd = 167
Time = 24, cwnd = 168,  
Time = 25:  packet loss is detected, so ssthresh will become half of current cwnd value, 
ssthresh = 168/2=84, cwnd=10 (reseted)
Time = 26: cwnd = 20
Time = 27, cwnd = 40
Time = 28, cwnd = 80
Final cwnd is = 80

Input arr[] = {12, 20, 31, 45}, ssthresh = 300, rtt = 50
Output: The final cwnd value is= 29
Explanation:
Time = 0: cwnd = 10
Time = 1: cwnd = 20
Time = 2, 3, 4: cwnd = 40, 80, 160
Time = 5: cwnd = 300 {cwnd can’t get doubled because 320>300, it will cross the ssthresh. It can go max upto ssthresh}
Time = 6-11: cwnd = 301-306
Time = 12: cwnd = 10 (reseted), and ssthresh = 306/2=153 {Packet loss}
Time = 13: cwnd = 20
Time = 14: cwnd = 40
Time = 15: cwnd = 80
Time = 16: cwnd = 153, {cwnd can’t get doubled because 160>153, it will cross the ssthresh. It can go max upto ssthresh}
Time = 17: cwnd = 154
Time = 18: cwnd = 155
Time = 19: cwnd = 156
Time = 20:  cwnd = 10 (reseted), ssthresh = 156/2 = 78   {Packet loss}
Time = 21: cwnd = 20
Time = 22: cwnd = 20
Time = 23: cwnd = 40
Time = 24: cwnd = 78, {cwnd can’t get doubled because 80>78, it will cross the ssthresh. It can go max upto ssthresh}
Time = 25-30: cwnd = (78+1=79) – (78+6=84) 
Time = 31: cwnd = 10 (reseted), ssthresh = 84/2 = 42   {Packet loss}
Time = 32: cwnd = 20
Time = 33, cwnd = 40
Time = 34, cwnd = 42, {cwnd can’t get doubled because 80>42, it will cross the ssthresh. It can go max upto ssthresh}
Time = 35-44: cwnd = 43 – 52
Time = 45: cwnd = 10 (reseted), ssthresh = 52/2 = 26   {Packet loss}
Time = 46: cwnd = 20
Time = 47: cwnd = 26 {cwnd can’t get doubled because 40>26, it will cross the ssthresh. It can go max upto ssthresh}
Time = 48-50: cwnd = 27-29
The final cwnd value is= 29

方法：想法是牢记所有约束并编写代码以最小的时间和空间复杂度运行。按照以下步骤操作：

• 当连接处于活动状态时，遍历所有时间单位。
• 将下一个丢包时间存储在可变超时中
• 检查当前时间是否等于超时。如果是，则减少ssthresh = cwnd/2并将cwnd 重置为 10 。
  • 如果 cwnd 小于ssthresh ，则将cwnd值加倍。
  • 如果cwnd的两倍大于ssthresh ，则设置cwnd=ssthresh。
  • 如果cwnd大于ssthresh ，则每次将cwnd增加 1。
• 循环终止后返回最终的cwnd值。

下面是上述方法的实现。

C++

// C++ code to find the final size
// of congestion window in TCP TAHOE
 
#include 
using namespace std;
 
// TCP Tahoe Utility function
int tcpTahoeCongestionWindow(
    int initcwnd, int cwnd,
    int ssthresh, int rtt,
    vector time)
{
    int ind = 0, timeout = time[ind];
    for (int t = 1; t <= rtt; t++) {
 
        // Packet loss occurs.
        // Reduce ssthresh to half of
        // current cwnd value.
        // Reset cwnd to 10
        if (t == timeout) {
            ssthresh = cwnd / 2;
            cwnd = initcwnd;
            timeout = time[++ind];
            continue;
        }
 
        // Threshold is not reached.
        // Keep doubling
        if (cwnd < ssthresh)
            cwnd = min(2 * cwnd,
                       ssthresh);
 
        // Threshold is reached.
        // Increase additively.
        else
            cwnd += 1;
    }
 
    // Return final cwnd value.
    return cwnd;
}
 
// Driver code
int main()
{
    int initcwnd = 10, cwnd = 10;
    int ssthresh = 300;
    int rtt = 50;
    vector time{ 12, 20, 31, 45 };
 
    // Function call
    cwnd = tcpTahoeCongestionWindow(
        initcwnd, cwnd,
        ssthresh, rtt, time);
    cout << cwnd;
    return 0;
}

Javascript

    // JavaScript code for the above approach
 
    // TCP Tahoe Utility function
    function tcpTahoeCongestionWindow(
        initcwnd, cwnd,
        ssthresh, rtt,
        time) {
        let ind = 0, timeout = time[ind];
        for (let t = 1; t <= rtt; t++) {
 
            // Packet loss occurs.
            // Reduce ssthresh to half of
            // current cwnd value.
            // Reset cwnd to 10
            if (t == timeout) {
                ssthresh = Math.floor(cwnd / 2);
                cwnd = initcwnd;
                timeout = time[++ind];
                continue;
            }
 
            // Threshold is not reached.
            // Keep doubling
            if (cwnd < ssthresh)
                cwnd = Math.min(2 * cwnd,
                    ssthresh);
 
            // Threshold is reached.
            // Increase additively.
            else
                cwnd += 1;
        }
 
        // Return final cwnd value.
        return cwnd;
    }
 
    // Driver code
    let initcwnd = 10, cwnd = 10;
    let ssthresh = 300;
    let rtt = 50;
    let time = [12, 20, 31, 45];
 
    // Function call
    cwnd = tcpTahoeCongestionWindow(
        initcwnd, cwnd,
        ssthresh, rtt, time);
    document.write(cwnd);
 
 // This code is contributed by Potta Lokesh

输出

Final congestion window size = 29

时间复杂度： O(N)，N是连接活跃的时间。
辅助空间： O(1)