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3. Consider the M/M/1 queue discussed in class. Assume that packets arrive to a queue with average arrival rate A [pkts/s]. The average service rate of the queue is denoted by µ [pkts/s]. (a) Write expressions for: (i) the mean time between packet arrivals to the queue, i.e., the average inter-arrival time; and (ii) the mean service time, i.e., the average time needed to transmit a packet onto the outgoing link. (b) Let N denote the number of packets in the system in steady-state. Suppose A = 850 and u = 1000. Find the smallest value of B such that P(N > B) < e = 10-4. Hint: Use MATLAB or some other computational tool (you could even use an Excel spreadsheet) to test different values of B.

3. Consider the M/M/1 queue discussed in class. Assume that packets arrive to a queue with average arrival rate A [pkts/s]. The average service rate of the queue is denoted by µ [pkts/s]. (a) Write expressions for: (i) the mean time between packet arrivals to the queue, i.e., the average inter-arrival time; and (ii) the mean service time, i.e., the average time needed to transmit a packet onto the outgoing link. (b) Let N denote the number of packets in the system in steady-state. Suppose A = 850 and u = 1000. Find the smallest value of B such that P(N > B) < e = 10-4. Hint: Use MATLAB or some other computational tool (you could even use an Excel spreadsheet) to test different values of B.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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3. Consider the M/M/1 queue discussed in class. Assume that packets arrive to a queue with average arrival rate A [pkts/s]. The average service rate of the queue is denoted by u [pkts/s]. (a) Write expressions for: (i) the mean time between packet arrivals to the queue, i.e., the average inter-arrival time; and (ii) the mean service time, i.e., the average time needed to transmit a packet onto the outgoing link. (b) Let N denote the number of packets in the system in steady-state. Suppose A and u = 850 %3D 1000. Find the smallest value of B such that P(N > B) < € = 10-4. Hint: Use MATLAB or some other computational tool (you could even use an Excel spreadsheet) to test different values of B.
Transcribed Image Text:3. Consider the M/M/1 queue discussed in class. Assume that packets arrive to a queue with average arrival rate A [pkts/s]. The average service rate of the queue is denoted by u [pkts/s]. (a) Write expressions for: (i) the mean time between packet arrivals to the queue, i.e., the average inter-arrival time; and (ii) the mean service time, i.e., the average time needed to transmit a packet onto the outgoing link. (b) Let N denote the number of packets in the system in steady-state. Suppose A and u = 850 %3D 1000. Find the smallest value of B such that P(N > B) < € = 10-4. Hint: Use MATLAB or some other computational tool (you could even use an Excel spreadsheet) to test different values of B.
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