Rate of transmission in a wireless LAN

[zak100]

Homework Statement

Consider the scenario shown in below, in which there are four wireless nodes, A, B, C, and D. The
radio coverage of the four nodes is shown via the dashed lines; all nodes share the same frequency. When A transmits, it can only be heard/received by B; when B transmits, both A and C can hear/receive from B; when C transmits, both B and D can hear/receive from C; when D transmits, only C can hear/receive from D.
A - - - - - - - - - - B - - - - - - - - - - C - - - - - - - - - - D
Suppose now that each node has an infinite supply of messages that it wants to send to each of the other nodes. If a message’s destination is not an immediate neighbor, then the message must be relayed. For example, if A wants to send to D, a message from A must first be sent to B, which then sends the message to C, which then sends the message to D. Time is slotted, with a message transmission time taking exactly one time slot, e.g., as in slotted Aloha. During a slot, a node can do one of the following: (i) send a message; (ii) receive a message (if exactly one message is being sent to it), (iii) remain silent. As always, if a node hears two or more simultaneous transmissions, a collision occurs and none of the transmitted messages are received successfully. You can assume here that there are no bit-level errors,
and thus if exactly one message is sent, it will be received correctly by those within the transmission radius of the sender.

(a) Suppose that A sends messages to B, and D sends messages to C. What is the combined
maximum rate (e.g., in terms of # messages/slot) at which data messages can flow from A to B and from D to C?

Relevant Equations

No Eq.

Hi,
It says that:
When A transmits, it can only be heard/received by B
when D transmits, only C can hear/receive from D.

Ans : 2 messages/slot

Please provide some reasoning for this answer.

Zulfi.

 

[sepcurio]

Hints:
If there is no communication between the pairs A-B and C-D, how many collisions will there be between those two pairs?

If A only transmits to B and not vice versa, is that half-duplex or full-duplex? How many collisions are possible?

The same with D to C. How many collisions are possible there?

Can the pair A-B transmit at the same time as D-C without collisions?

-----------------------

Spoiler: Don't click here until you've figured it out yourself first...

The explanation is quite simple really...

There is no traffic between B and C, so the two transmitter/receiver pairs, A-B and D-C, are essentially two isolated networks -- there is no communication between them and no chance for collisions between them.

Since each of those two isolated networks (A-B and D-C) is communicating in a single direction only (like a half-duplex channel) there is also no chance of collisions within each of those two channels. So there is no chance of collisions anywhere in the entire system. This means that no messages will be lost and every slot will have a successful transmission each time. Since there is one message transmission happening during each slot on each of those two isolated networks, there are 2 successful messages per slot.

There are some more complicated functions to determine transmission rates based on collision probabilities in this type of network, but those equations are not needed in this case because the problem can be defined so simply based on the conditions outlined in the question, i.e., the collision probability is zero.

 

[zak100]

Thanks you are right. There is no collision. Both D to C and A to B transmit at the same time. So 2 messages/slot.

Zulfi.

 

[sepcurio]

Did you figure that out from my hints, or did you click the spoiler button?

 

[zak100]

No I did not even notice your spoiler button. I was in a hurry. I had to just verify the answer.

Zulfi.