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.
a)
Refer the given data and figure from the question before start the answer:
Consider the data:
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:
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:
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:
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:
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:
Hence, The combined maximum rate is 1data message/2slots.