Matlab simulation

What to do:

◦ Implement the system model with a simple MAC protocol described in Problem 10.

◦ Collect the following simulation results while varying the value of probability p: A fraction of time slots for successful frame transmissions over the simulation time span of interest, which is essentially the probability that a given slot is successful for transmission and also called “channel utilization” or “efficiency”.

◦ Compare the simulation results with their corresponding theoretical results (solutions of Problem 10).

• Suggestions:

◦ Observe that each slot is always in one of three states: collision, transmission, and idle.

◦ The suggested number of nodes (or stations) is N=6, but you may want to change the number of nodes and see its impact on the channel utilization.

◦ You may want to run fairly long simulations to obtain smooth results. Also, you may want to repeat the same simulation multiple times and take an average over your simulation runs.

◦ To plot graphs, I suggest you to use MATLAB, but you can use a different graphing software program such as Excel, Gnuplot (Linux), and Origin.

• Project Logistics:

◦ The programming languages that you can use for this project is MATLAB.

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Here is question number 10:

Time is divided into slots, and there are N nodes to communicate with one

common base station. Suppose that each node always has a frame to send and attempts

to transmit the frame in each slot with probability p. If two or more frames collide or no

frame is transmitted in a slot, that slot is unsuccessful for transmission.

(a) What is the probability that a given slot is successful for transmission, i.e., any one

of N nodes successfully transmits a frame to the base station?

(b) Find the value of p that maximizes the probability (expression) obtained in (a), or

maximizes the efficiency of this communication method.

2

7. (20 points) Time is divided into slots, and there are N nodes to communicate with one
common base station. Suppose that each node always has a frame to send and attempts
to transmit the frame in each slot with probability p. If two or more frames collide or no
frame is transmitted in a slot, that slot is unsuccessful for transmission.
(a) What is the probability that a given slot is successful for transmission, i.e., any one
of N nodes successfully transmits a frame to the base station?
Solution: The probability a given node has a success is p(1 – p)N-1. Because there
are N nodes, the probability that any one of the N nodes has a success, say F(p), is
F(p) = Np(1 – p)N-1
This can also be obtained from the Binomial distribution as follows.
F(p) =
()P(1
|p(1 – p) – = NP(1 – 2)^-1.
(b) Find the value of p that maximizes the probability (expression) obtained in (a), or
maximizes the efficiency of this communication method.
Solution: The value of p* leading to the maximum probability F(p*) is the value
of p for which the derivative of F(p) with respect to p is equal to zero, so it can be
obtained as follows.
1
N(1 – p)N-1 – N(N − 1)p(1 – p)N+2 = = 0 + p* =
N
where leads to the maximum probability
N-1
F(p*) =
1 = (1-5)