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 = 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) 850 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 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 = 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) 850 to test different values of B.
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
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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 = 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.
4. Consider the M/M/1 queue from Problem 3.
(a) Find an expression for E[N], i.e., the average number of packets in the system in steady-
state. For the values of A and µ specified in Problem 4(b), compute the value of E[N].
What happens when A→ µ?
(b) Find an expression for Var[N], i.e., the variance of the number of packets in the system
in steady-state. For the values of A and u specified in Problem 4(b), compute the value
of Var[N].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa80eb220-b198-4f3d-81bb-2cbd72fe9990%2Fcfefca3c-0f13-4871-85fe-6baa42457865%2F14a2qi_processed.png&w=3840&q=75)
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 = 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.
4. Consider the M/M/1 queue from Problem 3.
(a) Find an expression for E[N], i.e., the average number of packets in the system in steady-
state. For the values of A and µ specified in Problem 4(b), compute the value of E[N].
What happens when A→ µ?
(b) Find an expression for Var[N], i.e., the variance of the number of packets in the system
in steady-state. For the values of A and u specified in Problem 4(b), compute the value
of Var[N].
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