Consider the following network with given line speeds and lengths:   Assume the speed of light is 2×10^8 m/s, and that the processing and queuing delays are negligible.   Node A sends a 1400-byte frame to node C through node B. Suppose Node A starts sending the first bit of the frame at t=0. Answer the following questions:   a. At what time (t=?) node B receives the frame in full (i.e. the last bit)?   b. After node B receives the frame in full, then it will start sending the frame to node C. Determine the time (t=?) when node C receives the frame in full.    c. Suppose at this time node C sends a small acknowledgment back to node A. The transmission time for the acknowledgment is negligible. Calculate at what times (t=?) the acknowledgment arrives at nodes B and A.

Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter20: Queuing Theory
Section20.10: Exponential Queues In Series And Open Queuing Networks
Problem 8P
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Consider the following network with given line speeds and lengths:

 

Assume the speed of light is 2×10^8 m/s, and that the processing and queuing delays are negligible.

 

Node A sends a 1400-byte frame to node C through node B. Suppose Node A starts sending the first bit of the frame at t=0. Answer the following questions:

 

a. At what time (t=?) node B receives the frame in full (i.e. the last bit)?

 

b. After node B receives the frame in full, then it will start sending the frame to node C. Determine the time (t=?) when node C receives the frame in full. 

 

c. Suppose at this time node C sends a small acknowledgment back to node A. The transmission time for the acknowledgment is negligible. Calculate at what times (t=?) the acknowledgment arrives at nodes B and A. 

 

d. Assume after sending its frame, node A wait for the acknowledgment back from node C before sending the next frame. What is the average throughput (number of transmitted bits per second) of the data flow from node A to node C? 

 

NOTE: Transmission and Propagation times MUST be calculated for each network link and are cumulative.

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