A service company receives on average 4 service requests per day. The requests are received randomly according to Poisson process. The company has 2 service engineers and sends one engineer to attend each request. An engineer needs an exponentially distributed service time with the mean of day(s). The company's policy is to have maximum of 2 requests waiting in the queue If this number is reached, all incoming requests are rejected (sent to a competitor).
A service company receives on average 4 service requests per day. The requests are received randomly according to Poisson process. The company has 2 service engineers and sends one engineer to attend each request. An engineer needs an exponentially distributed service time with the mean of day(s). The company's policy is to have maximum of 2 requests waiting in the queue If this number is reached, all incoming requests are rejected (sent to a competitor).
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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![A service company receives on average 4 service requests per day.
The requests are received randomly according to Poisson process.
The company has 2 service engineers and sends one engineer to attend each request.
1
An engineer needs an exponentially distributed service time with the mean of
day(s).
2
The company's policy is to have maximum of 2 requests waiting in the queue
If this number is reached, all incoming requests are rejected (sent to a competitor).
Answer the following questions based on the information provide above:
(a) Using the Kendall's notation, indicate what type of queueing system it is:
(b) Compute the system state probabilities (provide at least 3 decimals):
Po =
P1=
P2 =
P3 =
Pa =
(c) Compute the expected total number of customer requests (waiting and served) in the system.
ELL] =
(d) Compute the expected number of accepted requests.
Aaccepted =
(e) Compute the expected total processing time (waiting + being served) for the accepted requests.
E[Time] =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbcc3f950-06bd-4299-ba75-b537b20a249b%2Ff801149e-3b9f-4d10-8e4a-578c252d7dde%2Fx4pyvne_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A service company receives on average 4 service requests per day.
The requests are received randomly according to Poisson process.
The company has 2 service engineers and sends one engineer to attend each request.
1
An engineer needs an exponentially distributed service time with the mean of
day(s).
2
The company's policy is to have maximum of 2 requests waiting in the queue
If this number is reached, all incoming requests are rejected (sent to a competitor).
Answer the following questions based on the information provide above:
(a) Using the Kendall's notation, indicate what type of queueing system it is:
(b) Compute the system state probabilities (provide at least 3 decimals):
Po =
P1=
P2 =
P3 =
Pa =
(c) Compute the expected total number of customer requests (waiting and served) in the system.
ELL] =
(d) Compute the expected number of accepted requests.
Aaccepted =
(e) Compute the expected total processing time (waiting + being served) for the accepted requests.
E[Time] =
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