1. In this problem, you are asked to analyze the following CSMA/CD MAC protocol where N nodes contend for accessing a shared channel. In this protocol, time is di- vided into contention slots, and all nodes are synchronized to the slots. In particular, at the beginning of each slot: Each node has a frame to transmit, and each node senses the channel If the channel is sensed idle, the node chooses to transmit with probability p (so, some nodes may not contend for the channel in this slot). If exactly one node chooses to transmit in the slot then it takes possession of the channel for a number of consecutive slots (including the current slot) . On the other hand, if the channel is busy then each other node refrains from transmitting its frame. A slot is productive if a single node can either start, or continue, transmitting its frame according to the protocol. Otherwise, a slot is unproductive. Denote by X the number of consecutive unproductive slots. X is a random variable. We want to estimate the average X as a function of N and p. To this end, you are required to write a program (in a programming language of your choice) to provide the following information, (a) Hand-in a printed version of your program (b) Use the obtained results to complete the following table. 0.05 0.1 0.2 0.3 0.4 0.5 0.60.7 N 10 N- 20 (c) Based on the obtained results, discuss the plausibility of having for each N a probability p where X attains a minimum value. Note: More remarks on the construction of the required program will be posted on the website, 1. In this problem, you are asked to analyze the following CSMA/CD MAC protocol where N nodes contend for accessing a shared channel. In this protocol, time is di- vided into contention slots, and all nodes are synchronized to the slots. In particular, at the beginning of each slot: Each node has a frame to transmit, and each node senses the channel If the channel is sensed idle, the node chooses to transmit with probability p (so, some nodes may not contend for the channel in this slot). If exactly one node chooses to transmit in the slot then it takes possession of the channel for a number of consecutive slots (including the current slot) . On the other hand, if the channel is busy then each other node refrains from transmitting its frame. A slot is productive if a single node can either start, or continue, transmitting its frame according to the protocol. Otherwise, a slot is unproductive. Denote by X the number of consecutive unproductive slots. X is a random variable. We want to estimate the average X as a function of N and p. To this end, you are required to write a program (in a programming language of your choice) to provide the following information, (a) Hand-in a printed version of your program (b) Use the obtained results to complete the following table. 0.05 0.1 0.2 0.3 0.4 0.5 0.60.7 N 10 N- 20 (c) Based on the obtained results, discuss the plausibility of having for each N a probability p where X attains a minimum value. Note: More remarks on the construction of the required program will be posted on the website