# Suppose that packets arrive from various sources to a statistical multiplexer that transmits the…

**Problem 1. (50 points)**

Suppose that packets arrive from various sources to a statistical multiplexer that transmits the packets over a 64 kbps PPP link. Suppose that the PPP frames have lengths that follow an exponential distribution with mean 1000 bytes and that the multiplexer can hold up to 100 packets at a time.

- Based on a reasonable assumption for a queue model, provide a formula for the average packet delay as a function of the packet arrival rate.
**Make sure to explain your assumption**. (10 points)

- Using
**Matlab**program, plot the average packet delay as a function of the packet arrival rate. (30 points).

(2.1) Generate a set of sample numerical data of the average packet delay for your plot and show how you generated them using the formula in (1). (15 points).

(2.2) Create your plot of the average packet delay as a function of the packet arrival rate using the set of sample data you generated in (2.1). Make sure you provide your sample numerical data on your plot.

**A plot WITHOUT numerical data will result in no points at all**. (15 points).

**Briefly**explain your plot above. (10 points)

**Problem 2. (50 points)**

Suppose that packets arrive from various sources to a statistical multiplexer that transmits the packets over a 1 Mbps PPP link. Also, suppose that the PPP frames have constant length of

*L* bytes and that the multiplexer can hold a very large number of packets at a time. Assume that each PPP frame contains a PPP, IP, and TCP header in addition to the user data.

- Based on a reasonable assumption for a queue model, provide a formula for the average packet delay as a function of the rate at which user information is transmitted.
**Make sure to explain your assumption**. (10 points)

- Using Matlab program, plot the average packet delay as a function of the rate at which user information is transmitted for
*L*= 250 bytes, 500 bytes, and 1000 bytes.

(2.1) Generate a set of sample numerical data of the average packet delay for your plot and show how you generated them using the formula in (1). (15 points).

(2.2) Create your plot of the average packet delay as a function of the packet arrival rate using the set of sample data you generated in (2.1). Make sure you provide your sample numerical data on your plot.

**A plot WITHOUT numerical data will result in no points at all**. (15 points).

**Briefly**explain your plot above. (10 points)

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