## computer networks – TCP congestion control problem

Assume that the maximum transmission window size for a TCP connection is 12000 bytes. Each packet consists of 2000 bytes. At some point, the connection is in a slow start phase with a current 4000 byte transmission window. Subsequently, the transmitter receives two acknowledgments. Assume no packets are lost and there are no waiting times. What is the maximum possible value of the current transmission window?

A) 4000 bytes

B) 8000 bytes

C) 10,000 bytes

D) 12000 bytes

In the congestion control algorithm, when we are in the slow start phase, after 1RTT (round trip time) if the window size exceeds the threshold when doubling, we set cwnd (current window size) = threshold or cwnd = 2 * cwnd?

How to solve this problem?

## Do multiple SSIDs affect congestion on Wi-Fi 6 networks?

Wi-Fi 6 has anti-congestion features, does this allow one to use an unlimited number * of SSID without causing interference?

* * A large number

## Optimization – Linear mathematical formulation of a congestion game.

I need to implement the following congestion game in AMPL:

Leave $$J = {1,2,3,4 }$$ be a set of jobs and leave $$M = {1,2,3 }$$ Be a set of machines.

• Work 1 can be solved by machines 1 and 2.
• Work 2 can be solved by machines 1 and 3.
• Work 3 can be solved by machines 2 and 3.
• Work 4 can be solved by machines 2 and 3.

Each job uses a single machine.

The time required by each machine to solve a job depends on its congestion (namely, the amount of different jobs assigned to the machine) as follows:

• Machine 1: $$time_1 =[1,3,5,7]$$
• Machine 2: $$time_2 =[2,4,6,8]$$
• Machine 3: $$time_3 =[3,4,5,6]$$

The element $$i$$ vector $$time_m$$ is equal to the time required by the machine $$m$$ given a congestion equal to $$i$$.

[e.g.] If machine 1 solves jobs 1 and 2, the congestion of the machine
1 is equal to 2, so the resolution of these works (1 and 2) requires
equal time to $$time_1 (2) = 3$$. (indexing starts from 1)

The objective is to solve all the works in such a way that the maximum time between the machines is minimal.

The problem with the implementation is that I need to use the variable "congestion" as an index and that is not allowed in AMPL.

Is there any way to implement this game as a linear problem in AMPL? What is the formulation of linear mathematical programming without using variables as indexes of the "time matrix" (the matrix has as rows) $$time_i$$)?