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# Find the final size of Congestion Window in TCP Tahoe

• Difficulty Level : Expert
• Last Updated : 04 Mar, 2022

Given the initial congestion window size cwnd, threshold value ssthresh, connection time rtt and an array arr where arr[i] implies the time when a packet loss is detected. The task is to find the final congestion window size when all the packet drops are being encountered by the sender.

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.

Examples:

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

Approach: The idea is to keep all the constraints in mind and write the code to run in minimum time and space complexity.Follow below steps:

• Traverse through all the time units when the connection is alive.
• Store the next packet loss time in variable timeout
• Check if the current time is equal to timeout. if it is, then reduce the ssthresh = cwnd/2 and reset cwnd to 10.
• If cwnd is less than ssthresh, then double the cwnd value.
• If by double of cwnd is greater than ssthresh then set cwnd=ssthresh.
• If cwnd is greater than ssthresh then increment cwnd by 1 per time.
• Return final cwnd value after the loop terminates.

Below is the implementation of the above approach.

## 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<``int``> ``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<``int``> ``time``{ 12, 20, 31, 45 };`   `    ``// Function call` `    ``cwnd = tcpTahoeCongestionWindow(` `        ``initcwnd, cwnd,` `        ``ssthresh, rtt, ``time``);` `    ``cout << cwnd;` `    ``return` `0;` `}`

## Javascript

 ``

Output

`Final congestion window size = 29`

Time complexity: O(N), N is the time of connection activeness.
Auxiliary Space: O(1)

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