## This problem has been solved!

# (1) Consider the following network topology shown in the following figure. We make the following assumptions: The transmission power at each node is the same. A simplified Free space radio model is adopted: Pr(d) = Pt/d2, where d is the distance between sender and receiver. Regarding the communication model considering SNR, we assume =1.25 (i.e. the condition for correct

(1) Consider the following network topology shown in the following figure. We make the following assumptions:

The transmission power at each node is the same.

A simplified Free space radio model is adopted: Pr(d) = Pt/d2, where d is the distance between sender and receiver.

Regarding the communication model considering SNR, we assume =1.25 (i.e. the condition for correct transmission is that the SNR at the receiver is not smaller than 1.25)

Regarding the simplified communication model without considering SNR, we assume d =1 (i.e. the condition for correct transmission is that the distance between the sender and the receiver is not larger than 1)

The nodes are distributed in the intersection points of a 2 * 2 square grid. The side of each grid is 1 meter. (i.e. the distance between 1 and 2 is 1 meter).

(a) With the first model (the one that considers SNR), what is the maximal number of successful, simultaneous transmissions that can occur in the network? Please list all possible simultaneous transmissions.

(b) With the simplified communication model, what is the maximal number of successful, simultaneous transmissions that can occur in the network? Please list all possible simultaneous transmissions.

(2) Consider a chain of n nodes as shown in the following figure. Assume that the distance between the adjacent nodes in the chain is d. Assume that IEEE 802.11 DCF protocol is used. Also, assume that a node can reliably receive the transmission from another node within distance d2 or less, and a node can sense the transmission from another node at distance at most d3, where d3 = 2 * d2. What is the maximum number of nodes that can reliably transmit message simultaneously when d = 0.5 * d2?

**Related Book For**

## A First Course in Differential Equations with Modeling Applications

11th edition

Authors: Dennis G. Zill

ISBN: 978-1305965720