The Men's Department.
$begingroup$
I was given this question to solve:
The Men's Department of a large store employs one tailor for customer's fitting. The number of customers requiring fitting has a mean arrival time rate of 24 per hour . Customers are fitted on a first come first served basis and are willing to wait for the tailor's service. The time it takes to fit a customer has a mean of 2 minutes.
What is the average number of customers in the fitting room?
How much time should a customer expect to spend in the fitting room ?
What percentage of the time is the tailors idle?.
This is how I approached the question :
I changed the 2 minutes to hours and had 1/30. Next I solved question one using queuing theory and the solution was 47 customers.
For the second question I had 2 hours per time .
But I am a bit confused as to how to get the approach in solving the third question.
Are my answers correct for question 1 and 2. And how will I get the answer to question 3.?
stochastic-processes queueing-theory
edited Dec 21 '18 at 0:10
Math1000
19k31745
asked Dec 20 '18 at 21:08
AstatineAstatine
86
$endgroup$
|
show 3 more comments
$begingroup$
I was given this question to solve:
The Men's Department of a large store employs one tailor for customer's fitting. The number of customers requiring fitting has a mean arrival time rate of 24 per hour . Customers are fitted on a first come first served basis and are willing to wait for the tailor's service. The time it takes to fit a customer has a mean of 2 minutes.
What is the average number of customers in the fitting room?
How much time should a customer expect to spend in the fitting room ?
What percentage of the time is the tailors idle?.
This is how I approached the question :
I changed the 2 minutes to hours and had 1/30. Next I solved question one using queuing theory and the solution was 47 customers.
For the second question I had 2 hours per time .
But I am a bit confused as to how to get the approach in solving the third question.
Are my answers correct for question 1 and 2. And how will I get the answer to question 3.?
stochastic-processes queueing-theory
edited Dec 21 '18 at 0:10
Math1000
19k31745
asked Dec 20 '18 at 21:08
AstatineAstatine
86
$endgroup$
$begingroup$
You could try a Poisson distribution.
$endgroup$
– Jam
Dec 20 '18 at 21:12
$begingroup$
It seems unreasonable to have $47$ customers waiting when the arrival rate is slower than the service rate. Please check. For the third, what happens at the end of the day? You can just take the number of customers received, count the $2$ minutes serving each one, and find the busy time. Presumably his idle time is the amount of time in the day less the busy time.
$endgroup$
– Ross Millikan
Dec 20 '18 at 21:13
$begingroup$
How then will I get the average customers, any idea will be appreciated
$endgroup$
– Astatine
Dec 20 '18 at 21:15
$begingroup$
How does a Poisson distribution apply in this case
$endgroup$
– Astatine
Dec 20 '18 at 21:16
$begingroup$
Queuing theory is what you want for the average customers, but I don't think you applied it correctly. If they average $2.5$ minutes between arrivals and $2$ minute service, most of the time he is done with one before the next arrives. You can't build up a long line.
$endgroup$
– Ross Millikan
Dec 20 '18 at 21:16
|
show 3 more comments
$begingroup$
I was given this question to solve:
The Men's Department of a large store employs one tailor for customer's fitting. The number of customers requiring fitting has a mean arrival time rate of 24 per hour . Customers are fitted on a first come first served basis and are willing to wait for the tailor's service. The time it takes to fit a customer has a mean of 2 minutes.
What is the average number of customers in the fitting room?
How much time should a customer expect to spend in the fitting room ?
What percentage of the time is the tailors idle?.
This is how I approached the question :
I changed the 2 minutes to hours and had 1/30. Next I solved question one using queuing theory and the solution was 47 customers.
For the second question I had 2 hours per time .
But I am a bit confused as to how to get the approach in solving the third question.
Are my answers correct for question 1 and 2. And how will I get the answer to question 3.?
stochastic-processes queueing-theory
edited Dec 21 '18 at 0:10
Math1000
19k31745
asked Dec 20 '18 at 21:08
AstatineAstatine
86
$endgroup$
I was given this question to solve:
The Men's Department of a large store employs one tailor for customer's fitting. The number of customers requiring fitting has a mean arrival time rate of 24 per hour . Customers are fitted on a first come first served basis and are willing to wait for the tailor's service. The time it takes to fit a customer has a mean of 2 minutes.
What is the average number of customers in the fitting room?
How much time should a customer expect to spend in the fitting room ?
What percentage of the time is the tailors idle?.
This is how I approached the question :
I changed the 2 minutes to hours and had 1/30. Next I solved question one using queuing theory and the solution was 47 customers.
For the second question I had 2 hours per time .
But I am a bit confused as to how to get the approach in solving the third question.
Are my answers correct for question 1 and 2. And how will I get the answer to question 3.?
stochastic-processes queueing-theory
stochastic-processes queueing-theory
edited Dec 21 '18 at 0:10
Math1000
19k31745
asked Dec 20 '18 at 21:08
AstatineAstatine
86
edited Dec 21 '18 at 0:10
Math1000
19k31745
asked Dec 20 '18 at 21:08
AstatineAstatine
86
edited Dec 21 '18 at 0:10
Math1000
19k31745
edited Dec 21 '18 at 0:10
Math1000
19k31745
edited Dec 21 '18 at 0:10
Math1000
19k31745
19k31745
asked Dec 20 '18 at 21:08
AstatineAstatine
86
asked Dec 20 '18 at 21:08
AstatineAstatine
86
asked Dec 20 '18 at 21:08
AstatineAstatine
86
86
$begingroup$
You could try a Poisson distribution.
$endgroup$
– Jam
Dec 20 '18 at 21:12
$begingroup$
It seems unreasonable to have $47$ customers waiting when the arrival rate is slower than the service rate. Please check. For the third, what happens at the end of the day? You can just take the number of customers received, count the $2$ minutes serving each one, and find the busy time. Presumably his idle time is the amount of time in the day less the busy time.
$endgroup$
– Ross Millikan
Dec 20 '18 at 21:13
$begingroup$
How then will I get the average customers, any idea will be appreciated
$endgroup$
– Astatine
Dec 20 '18 at 21:15
$begingroup$
How does a Poisson distribution apply in this case
$endgroup$
– Astatine
Dec 20 '18 at 21:16
$begingroup$
Queuing theory is what you want for the average customers, but I don't think you applied it correctly. If they average $2.5$ minutes between arrivals and $2$ minute service, most of the time he is done with one before the next arrives. You can't build up a long line.
$endgroup$
– Ross Millikan
Dec 20 '18 at 21:16
|
show 3 more comments
$begingroup$
You could try a Poisson distribution.
$endgroup$
– Jam
Dec 20 '18 at 21:12
$begingroup$
It seems unreasonable to have $47$ customers waiting when the arrival rate is slower than the service rate. Please check. For the third, what happens at the end of the day? You can just take the number of customers received, count the $2$ minutes serving each one, and find the busy time. Presumably his idle time is the amount of time in the day less the busy time.
$endgroup$
– Ross Millikan
Dec 20 '18 at 21:13
$begingroup$
How then will I get the average customers, any idea will be appreciated
$endgroup$
– Astatine
Dec 20 '18 at 21:15
$begingroup$
How does a Poisson distribution apply in this case
$endgroup$
– Astatine
Dec 20 '18 at 21:16
$begingroup$
Queuing theory is what you want for the average customers, but I don't think you applied it correctly. If they average $2.5$ minutes between arrivals and $2$ minute service, most of the time he is done with one before the next arrives. You can't build up a long line.
$endgroup$
– Ross Millikan
Dec 20 '18 at 21:16
$begingroup$
You could try a Poisson distribution.
$endgroup$
– Jam
Dec 20 '18 at 21:12
$begingroup$
You could try a Poisson distribution.
$endgroup$
– Jam
Dec 20 '18 at 21:12
$begingroup$
It seems unreasonable to have $47$ customers waiting when the arrival rate is slower than the service rate. Please check. For the third, what happens at the end of the day? You can just take the number of customers received, count the $2$ minutes serving each one, and find the busy time. Presumably his idle time is the amount of time in the day less the busy time.
$endgroup$
– Ross Millikan
Dec 20 '18 at 21:13
$begingroup$
It seems unreasonable to have $47$ customers waiting when the arrival rate is slower than the service rate. Please check. For the third, what happens at the end of the day? You can just take the number of customers received, count the $2$ minutes serving each one, and find the busy time. Presumably his idle time is the amount of time in the day less the busy time.
$endgroup$
– Ross Millikan
Dec 20 '18 at 21:13
$begingroup$
How then will I get the average customers, any idea will be appreciated
$endgroup$
– Astatine
Dec 20 '18 at 21:15
$begingroup$
How then will I get the average customers, any idea will be appreciated
$endgroup$
– Astatine
Dec 20 '18 at 21:15
$begingroup$
How does a Poisson distribution apply in this case
$endgroup$
– Astatine
Dec 20 '18 at 21:16
$begingroup$
How does a Poisson distribution apply in this case
$endgroup$
– Astatine
Dec 20 '18 at 21:16
$begingroup$
Queuing theory is what you want for the average customers, but I don't think you applied it correctly. If they average $2.5$ minutes between arrivals and $2$ minute service, most of the time he is done with one before the next arrives. You can't build up a long line.
$endgroup$
– Ross Millikan
Dec 20 '18 at 21:16
$begingroup$
Queuing theory is what you want for the average customers, but I don't think you applied it correctly. If they average $2.5$ minutes between arrivals and $2$ minute service, most of the time he is done with one before the next arrives. You can't build up a long line.
$endgroup$
– Ross Millikan
Dec 20 '18 at 21:16
|
show 3 more comments
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3047965%2fthe-mens-department%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3047965%2fthe-mens-department%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
You could try a Poisson distribution.
$endgroup$
– Jam
Dec 20 '18 at 21:12
$begingroup$
It seems unreasonable to have $47$ customers waiting when the arrival rate is slower than the service rate. Please check. For the third, what happens at the end of the day? You can just take the number of customers received, count the $2$ minutes serving each one, and find the busy time. Presumably his idle time is the amount of time in the day less the busy time.
$endgroup$
– Ross Millikan
Dec 20 '18 at 21:13
$begingroup$
How then will I get the average customers, any idea will be appreciated
$endgroup$
– Astatine
Dec 20 '18 at 21:15
$begingroup$
How does a Poisson distribution apply in this case
$endgroup$
– Astatine
Dec 20 '18 at 21:16
$begingroup$
Queuing theory is what you want for the average customers, but I don't think you applied it correctly. If they average $2.5$ minutes between arrivals and $2$ minute service, most of the time he is done with one before the next arrives. You can't build up a long line.
$endgroup$
– Ross Millikan
Dec 20 '18 at 21:16