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Authors:
James F. Kurose, Keith W. Ross
Chapter:
Wireless And Mobile Networks
Exercise:
Problems
Question:8 | ISBN:9780132856201 | Edition: 6

Question

Consider the scenario shown in Figure 6.33, 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. 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 imme- diate 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 now that an omniscient controller (i.e., a controller that knows the state of every node in the network) can command each node to do whatever it (the omniscient controller) wishes, i.e., to send a message, to receive a message, or to remain silent. Given this omniscient controller, what is the maximum rate at which a data message can be transferred from C to A, given that there are no other messages between any other source/destination pairs?



b. Suppose now that A sends messages to B, and D sends messages to C. What is the combined maximum rate at which data messages can flow from A to B and from D to C?

c. Suppose now that A sends messages to B, and C sends messages to D. What is the combined maximum rate at which data messages can flow from A to B and from C to D?

d. Suppose now that the wireless links are replaced by wired links. Repeat questions (a) through (c) again in this wired scenario.

e. Now suppose we are again in the wireless scenario, and that for every data message sent from source to destination, the destination will send an ACK message back to the source (e.g., as in TCP). Also suppose that each ACK message takes up one slot. Repeat questions (a) – (c) above for this scenario.

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Answer

a)

 

Refer the  given data and figure from the question before start the answer:

Consider the data:

  • Assume  that an omniscient controller (i.e., 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.
  • So, consider the four wireless nodes, A, B, C, and D in the figure.  The node  'C' send a data message to 'B'  is a 1 slot and  the node 'B' received message and send same data message to node 'A' is 2nd slot.
  • Here, given that there are no other messages between any other source/destination pairs. That means, 1 message per 2 slots.

Hence,  the maximum rate at which a data message can be transferred from C to A in omniscient controller is 1 data message/2 slots.

 

b)

 

Given data:

  • Take the four wireless nodes, A, B, C, and D in the figure. Assume that wireless node 'A' sends messages to node 'B;, and the node 'D' sends messages to node 'C'. 
  • Here, data messages can flow from A to B is a 1 slot and send another data message from D to C is a same slot. 
  • That means, 2 data messages per 1 slot.

 

Hence, the combined maximum rate at which data messages can flow from A to B and from D to C is 2 data messages/1slot.

 

c)

 

Given data:

  • Take the four wireless nodes, A, B, C, and D in the figure.  Assume the wireles node "A" sends messages to  node "B", and the node "C" sends messages to the node "D".
  • Here, observed that  the data messages can flow from the node 'A' to node 'B' and from the node'C' to the node 'D'. That is, only one data message can be transmitted successfully per each time slot.
  • That means, 1 data messages per 1 slot.

 

Hence, the combined maximum rate at which data messages can flow from A to B and from C to D is 1data message/1slot.

 

d)

 

Given data:

      The wireless links A, B, C, and D  are replaced by wired links.

 

For part (a):

The  maximum rate at which a data message can be transferred from C to A in omniscient controller is 1 data message/2 slots.

The reason is that, the wireless links are replaced with wires, node C is only connected to the node B      and node B is connected to  node A. So, 1 data message/2 slots. No difference found for wirlesslink and wired link nodes for this case.

 

For part (b):

The combined maximum rate at which data messages can flow from A to B and from D to C is 2 data messages/1slot.

The main reason that, the wired node A is directly connected to the wired node B and the wired node  D is connected to the the wired node C. So both A and D can send messages simultaneously in one slot. So, 2 data message/2 slot. No difference found for wirlesslink and wired link nodes for this case.

 

For part (c):

The combined maximum rate at which data messages can flow from A to B and from C to D is 1data message/1slot.

The main reason is that, the wired links are not facing any interference problem. So, the two transmissions from the wired node 'A' to wired node 'B' and the wired node 'C' to  the wired node 'D'. So, 1 data message per 1 slot occured.

 

e)

 

Given scenario of wireless link nodes:

Every data message sent from source to destination, the destination will send an ACK(Acknowledgment) message back to the source. Assume each ACK message takes up one slot.

 

For part (a):

The  maximum rate at which a data message can be transferred from C to A in omniscient controller is 1 data message/4 slots.

Explanation:

The following steps are send a data message from C to A is as follows:

  • From the wireless node 'C' to wireless node 'B'  as  considered 1 slot.
  • The node 'B' recieved data message and send same data message  to wireless node 'A' as consider 2slot.
  • The node 'A' recieved data message as consider acknolwegement and send acknowlegement message   to wireless node 'B' as consider  3 slot.
  • The node 'B' recieved acknowledgement message and send to node 'C' as consider 4 slot.

Hence, the  maximum rate   1 data message/4 slots.

 

 

For part (b):

The combined maximum rate at which data messages can flow from A to B and from D to C is 2 data messages/2 slots.

Expanation:

  • The node 'A' and  node 'D' will send the data in the same time slot.
  • In turn, the node 'B' and node 'C' send the acknowledgement the node 'A'  cannot. 
  • Here, the node C’s transmission and D cannot here B’s transmission. So, the nodes 'A' and 'D' receive acknowlegement message due to interference problem.

Hence, the combined maximum rate is 2 data messages/2 slots.

 

 

For part (c):

The combined maximum rate at which data messages can flow from A to B and from C to D is 1data message/2slots.

Explanation:

  • The transfer a data message from the node 'A' to  node 'B' and the node 'C' to the node 'D'  as 1 slot and above sequence of transmission is repeated, until  the node 'C' transfered the total data message to D as 2 slot. So, 1 data message per 2 slots

Hence, The combined maximum rate is 1data message/2slots.

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