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7.3-1. Overlapping 802.11 wireless networks (a)Consider the scenario shown below in which there are four wireless nodes, A, B, C, and D. The radio coverage of the four nodes is shown via the shaded ovals; 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. If a node hears two simultaneous transmissions at a time, the messages interfere at that receiver, even through they may not interfere at other receivers, where only one of the messages is heard.[Make sure you understand this paragraph.]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 heard at a receiver, it will be received correctly at that receiver.Suppose now that an omniscient controller (e.g., a controller that knows the state of every node in the network) can command each node to do whatever it (the omniscient controller) wishes, that is, to send a message, to receive a message, or to remain silent. Given this omniscient controller, what is the maximum rate at which messages can be transferred from C to A, given that there are no other messages between any other source/destination pairs?Group of answer choices0.5 messages/slot (i.e., 1 message every two slots).1 message/slot.2 messages/slot.0.25 messages/slot (i.e., one message every four slots).

Question

7.3-1. Overlapping 802.11 wireless networks (a)Consider the scenario shown below in which there are four wireless nodes, A, B, C, and D. The radio coverage of the four nodes is shown via the shaded ovals; 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. If a node hears two simultaneous transmissions at a time, the messages interfere at that receiver, even through they may not interfere at other receivers, where only one of the messages is heard.[Make sure you understand this paragraph.]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 heard at a receiver, it will be received correctly at that receiver.Suppose now that an omniscient controller (e.g., a controller that knows the state of every node in the network) can command each node to do whatever it (the omniscient controller) wishes, that is, to send a message, to receive a message, or to remain silent. Given this omniscient controller, what is the maximum rate at which messages can be transferred from C to A, given that there are no other messages between any other source/destination pairs?Group of answer choices0.5 messages/slot (i.e., 1 message every two slots).1 message/slot.2 messages/slot.0.25 messages/slot (i.e., one message every four slots).

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Solution

The maximum rate at which messages can be transferred from C to A, given that there are no other messages between any other source/destination pairs, is 0.5 messages/slot (i.e., 1 message every two slots).

Here's why:

  1. In the first time slot, C sends a message to B.
  2. In the second time slot, B sends that message to A.

So, it takes two time slots to send a message from C to A. Therefore, the rate is 0.5 messages per slot.

This problem has been solved

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