Problem $5$

$[8$ points$]($a$)$ Shown below is a multiplexer. Assume the data is transmitted right most

character first $($i$.$e$.,T$ is sent first in source $1).$

$(1)$Draw a diagram showing the character data sent in each of the frames if the

MUX is a synchronous TDM multiplexer.

$(2)$ Draw a diagram showing the character data sent in each of the frames if the

MUX is an asynchronous TDM multiplexer with a frame size of three characters.

$($b$)$ A company has its main computer in San Francisco, CA$,$ and regional offices in New

York, NY and Chicago, IL$.$ The company has four $300$ bps terminals in New York, and

three $1200$ bps$,$ two $4800$ bps$,$ and two $9600$ bps terminals in Chicago. The company

wants to connect all of the New York terminals along with the Chicago terminals to a

computer in San Francisco.

Assume that all terminals require immediate access to the computers $($i$.$e$.$ no polling is

allowed$)$ and voice grade circuits with a maximum data rate of $33,600bps$ are being

used. The maximum data rate of a voice grade line using an FDM is $2000$ bps$.$ The

maximum data rate of devices using an STDM equals twice the data rate of the voice

grade line. The costs for each circuit is as follows: NY$-$Chicago $$\frac{800}{?}$ month, NY$-$San

Francisco $$\frac{1500}{?}$ month, and Chicago$-$San Francisco $$\frac{1200}{?}$ month. The cost for the

communications equipment is $$\frac{25}{?}$ month for each FDM$,$ $$\frac{50}{?}$ month for each TDM$,$ and

$$75/$month for each STDM$.$

$[6$ points$](1)$ Find the minimum cost network i$.$e$.,$ the one where the total cost of the

communications circuits and equpment is the lowest, and draw a diagram of the

configuration.

$[6$ points$](2)$ The company wants to add two $1200$ bps$,$ and two $2400$ bps terminal in

New York to access the San Francisco computer. Find the new minimum cost network

and draw a diagram of this configuration.