Consider two servers that are in a row so that the client is first served on server 1, from where the client then moves to server 2. On both servers, clients are served on a first-come, first-served basis (FIFO). Customer B arrives at the first server so that customer A is already being served there. B must therefore wait until A has been served to the end on server 1 and moves on to server 2. It is assumed that the service times of the customers on server 1 and 2 are exponentially distributed and independent, so that the average service time on server 1 is 4 ms and on server 2, respectively, 1 ms. After customer B, there will be no new customers. (Hint: Properties of the exponential distribution and the dynamics of Markov processes) a) What is the average remaining delay of customer A in the system? That is, how long does it take on average for client A to leave server 2 when client B has arrived? (Hint: Customer A's delay does not depend on customer B.) b) What is the average total delay for customer B? So how long does it take on average for customer B to exit the system? (Hint: The possible events that follow after client A moves are B moves to server 2 before A's service ends there, or B moves to server 2 and A is still there. What are the probabilities of these events and how do they affect B's latency?) [Answer: 46/5]
Consider two servers that are in a row so that the client is first served on server 1, from where the client then moves to server 2. On both servers, clients are served on a first-come, first-served basis (FIFO). Customer B arrives at the first server so that customer A is already being served there. B must therefore wait until A has been served to the end on server 1 and moves on to server 2. It is assumed that the service times of the customers on server 1 and 2 are exponentially distributed and independent, so that the average service time on server 1 is 4 ms and on server 2, respectively, 1 ms. After customer B, there will be no new customers. (Hint: Properties of the exponential distribution and the dynamics of Markov processes) a) What is the average remaining delay of customer A in the system? That is, how long does it take on average for client A to leave server 2 when client B has arrived? (Hint: Customer A's delay does not depend on customer B.) b) What is the average total delay for customer B? So how long does it take on average for customer B to exit the system? (Hint: The possible events that follow after client A moves are B moves to server 2 before A's service ends there, or B moves to server 2 and A is still there. What are the probabilities of these events and how do they affect B's latency?) [Answer: 46/5]
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![Consider two servers that are in a row so that the client is first served on server 1, from where the client then moves to server
2. On both servers, clients are served on a first-come, first-served basis (FIFO). Customer B arrives at the first server so that
customer A is already being served there. B must therefore wait until A has been served to the end on server 1 and moves on
to server 2. It is assumed that the service times of the customers on server 1 and 2 are exponentially distributed and
independent, so that the average service time on server 1 is 4 ms and on server 2, respectively, 1 ms. After customer B, there
will be no new customers. (Hint: Properties of the exponential distribution and the dynamics of Markov processes)
a) What is the average remaining delay of customer A in the system? That is, how long does it take on average for client A to
leave server 2 when client B has arrived? (Hint: Customer A's delay does not depend on customer B.)
b) What is the average total delay for customer B? So how long does it take on average for customer B to exit the system?
(Hint: The possible events that follow after client A moves are B moves to server 2 before A's service ends there, or B moves
to server 2 and A is still there. What are the probabilities of these events and how do they affect B's latency?) [Answer: 46/5]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf116950-eb0d-47db-a7d5-7b3c212f8b61%2Fbdf42501-f8e4-4645-8b22-b1cd29dbf8f1%2Flw1rg0d_processed.png&w=3840&q=75)
Transcribed Image Text:Consider two servers that are in a row so that the client is first served on server 1, from where the client then moves to server
2. On both servers, clients are served on a first-come, first-served basis (FIFO). Customer B arrives at the first server so that
customer A is already being served there. B must therefore wait until A has been served to the end on server 1 and moves on
to server 2. It is assumed that the service times of the customers on server 1 and 2 are exponentially distributed and
independent, so that the average service time on server 1 is 4 ms and on server 2, respectively, 1 ms. After customer B, there
will be no new customers. (Hint: Properties of the exponential distribution and the dynamics of Markov processes)
a) What is the average remaining delay of customer A in the system? That is, how long does it take on average for client A to
leave server 2 when client B has arrived? (Hint: Customer A's delay does not depend on customer B.)
b) What is the average total delay for customer B? So how long does it take on average for customer B to exit the system?
(Hint: The possible events that follow after client A moves are B moves to server 2 before A's service ends there, or B moves
to server 2 and A is still there. What are the probabilities of these events and how do they affect B's latency?) [Answer: 46/5]
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