You are a network administrator of a company, where there are 40 users in total sharing a 20 Mbps network. On average, each user is active 12% of the time and needs 1 Mbps during active transmission. If the network uses packet switching technology, derive the probability that a user will not be able to obtain the network service immediately. (Hint: Show your answer with a formula containing a sum of multiple probabilities.) (5 Marks) (b) Consider a 12-bit data sequence 101000001111 and a generator polynomial g(x)= x + x +1 (1) Suppose the transmitter uses Differential Encoding as the line coding scheme, plot the encoded signal of the transmitted codeword. Assume the first bit is encoded as V+. (ii) Find the following three undetectable error patterns by using this generator polynomial: a 2-bit error, a 3-bit error, a 4-bit error. (12 Marks) (c) Use Bipolar with 8 Zeros Substitution (B8ZS) as an example to briefly explain the four design goals of a scramble code. (4 Marks) (d) Perform de-framing and byte de-stuffing for the following sequence that is to be received by the receiver. Note that the sequence is represented in hexadecimal format. Show your final answer in hexadecimal format. 7E7D5ED57D5DA7D87E (4 Marks) (b) Consider a case where sender A wants to send an M-bit message to receiver B via two store-and-forward switches and three links by using pipelining technique as shown in Figure 3. Each packet consists of a P-bit data payload and an H-bit header. Ignore the processing delay and queuing delay at all the nodes. Assume M is a multiple of P and A can send one packet after another without waiting for the acknowledgement from B. L2L3 Figure 3 For the two cases below, calculate the total delay experienced by the M-bit message. (i) (ii) Case 1: L1: rate=2Rbps, length = 2D meters, propagation speed = V meters/sec L2: rate = Rbps, length =D meters, propagation speed = V meters/sec L3: rate = 4Rbps, length = 40 meters, propagation speed = V meters/sec Case 2: L1: rate = 2R bps, length = 20 meters, propagation speed=V meters/sec L2: rate = 4R bps, length =D meters, propagation speed = V meters/sec L3: rate= R bps, length = 40 meters, propagation speed = V meters/sec (10 Marks) Consider a connection between two sites A and B to be a 100 Mbps point-to-point data link, via which A transmits data frames to Band B sends out acknowledgement (ACK) frame for every data frame that it receives successfully Each data frame is 500-byte long, of which 50 bytes is the header length. Each ACK frame is 50-byte long. Stop and Wait ARQ (Automatic Repeat reQuest) is used with a BER (bit error rate) of 10 in both data frame and ACK frame. The link is 1.1 km long and the propagation speed along the link is 2.2 x 10 meters/sec. Assume that B applies a processing delay of 2 * 10 sec to each data frame it receives for error checking purpose but the nodal processing delay at A is always negligible. (1) If A has a large set of 18,000,000 -- byte messages to send to B. calculate the average total delay of sending one such message successfully from A to B. (ii) Compute the effective throughput of data payload in Mbps of this data link You are a network administrator of a company, where there are 40 users in total sharing a 20 Mbps network. On average, each user is active 12% of the time and needs 1 Mbps during active transmission. If the network uses packet switching technology, derive the probability that a user will not be able to obtain the network service immediately. (Hint: Show your answer with a formula containing a sum of multiple probabilities.) (5 Marks) (b) Consider a 12-bit data sequence 101000001111 and a generator polynomial g(x)= x + x +1 (1) Suppose the transmitter uses Differential Encoding as the line coding scheme, plot the encoded signal of the transmitted codeword. Assume the first bit is encoded as V+. (ii) Find the following three undetectable error patterns by using this generator polynomial: a 2-bit error, a 3-bit error, a 4-bit error. (12 Marks) (c) Use Bipolar with 8 Zeros Substitution (B8ZS) as an example to briefly explain the four design goals of a scramble code. (4 Marks) (d) Perform de-framing and byte de-stuffing for the following sequence that is to be received by the receiver. Note that the sequence is represented in hexadecimal format. Show your final answer in hexadecimal format. 7E7D5ED57D5DA7D87E (4 Marks) (b) Consider a case where sender A wants to send an M-bit message to receiver B via two store-and-forward switches and three links by using pipelining technique as shown in Figure 3. Each packet consists of a P-bit data payload and an H-bit header. Ignore the processing delay and queuing delay at all the nodes. Assume M is a multiple of P and A can send one packet after another without waiting for the acknowledgement from B. L2L3 Figure 3 For the two cases below, calculate the total delay experienced by the M-bit message. (i) (ii) Case 1: L1: rate=2Rbps, length = 2D meters, propagation speed = V meters/sec L2: rate = Rbps, length =D meters, propagation speed = V meters/sec L3: rate = 4Rbps, length = 40 meters, propagation speed = V meters/sec Case 2: L1: rate = 2R bps, length = 20 meters, propagation speed=V meters/sec L2: rate = 4R bps, length =D meters, propagation speed = V meters/sec L3: rate= R bps, length = 40 meters, propagation speed = V meters/sec (10 Marks) Consider a connection between two sites A and B to be a 100 Mbps point-to-point data link, via which A transmits data frames to Band B sends out acknowledgement (ACK) frame for every data frame that it receives successfully Each data frame is 500-byte long, of which 50 bytes is the header length. Each ACK frame is 50-byte long. Stop and Wait ARQ (Automatic Repeat reQuest) is used with a BER (bit error rate) of 10 in both data frame and ACK frame. The link is 1.1 km long and the propagation speed along the link is 2.2 x 10 meters/sec. Assume that B applies a processing delay of 2 * 10 sec to each data frame it receives for error checking purpose but the nodal processing delay at A is always negligible. (1) If A has a large set of 18,000,000 -- byte messages to send to B. calculate the average total delay of sending one such message successfully from A to B. (ii) Compute the effective throughput of data payload in Mbps of this data link