Estimate the shops total revenue per day.
$begingroup$
You are a frequent customer at a coffee shop, where you typically wait
3 minutes to be served. Furthermore, on average, you spend 4 dollars
per visit. Over many months you estimate that on a typical day there
are 20 customers in the shop, which is open from 6 a.m to 10 p.m.
Estimate the shops total revenue per day.
I'm not sure how I should identify this problem. It seems to lean towards being a queing process, M/M/1 and the queue length on average is 20 individuals from 6 a.m to 10.p.m. But I don't know how the customers arrive to the shop but since there should always be 20 customers in the shop then they have to leave with the same rate as they arrive.
Am I supposed to assume that the customers leave right after being served, that is each 3 minutes? I don't know the distribution of any of these times because it's not stated whether the arrival follows a Poisson process or not.
How to go about this?
probability-theory markov-chains queueing-theory
asked Jan 11 at 14:17
ParsevalParseval
3,0741719
$endgroup$
add a comment |
$begingroup$
You are a frequent customer at a coffee shop, where you typically wait
3 minutes to be served. Furthermore, on average, you spend 4 dollars
per visit. Over many months you estimate that on a typical day there
are 20 customers in the shop, which is open from 6 a.m to 10 p.m.
Estimate the shops total revenue per day.
I'm not sure how I should identify this problem. It seems to lean towards being a queing process, M/M/1 and the queue length on average is 20 individuals from 6 a.m to 10.p.m. But I don't know how the customers arrive to the shop but since there should always be 20 customers in the shop then they have to leave with the same rate as they arrive.
Am I supposed to assume that the customers leave right after being served, that is each 3 minutes? I don't know the distribution of any of these times because it's not stated whether the arrival follows a Poisson process or not.
How to go about this?
probability-theory markov-chains queueing-theory
asked Jan 11 at 14:17
ParsevalParseval
3,0741719
$endgroup$
add a comment |
$begingroup$
You are a frequent customer at a coffee shop, where you typically wait
3 minutes to be served. Furthermore, on average, you spend 4 dollars
per visit. Over many months you estimate that on a typical day there
are 20 customers in the shop, which is open from 6 a.m to 10 p.m.
Estimate the shops total revenue per day.
I'm not sure how I should identify this problem. It seems to lean towards being a queing process, M/M/1 and the queue length on average is 20 individuals from 6 a.m to 10.p.m. But I don't know how the customers arrive to the shop but since there should always be 20 customers in the shop then they have to leave with the same rate as they arrive.
Am I supposed to assume that the customers leave right after being served, that is each 3 minutes? I don't know the distribution of any of these times because it's not stated whether the arrival follows a Poisson process or not.
How to go about this?
probability-theory markov-chains queueing-theory
asked Jan 11 at 14:17
ParsevalParseval
3,0741719
$endgroup$
You are a frequent customer at a coffee shop, where you typically wait
3 minutes to be served. Furthermore, on average, you spend 4 dollars
per visit. Over many months you estimate that on a typical day there
are 20 customers in the shop, which is open from 6 a.m to 10 p.m.
Estimate the shops total revenue per day.
I'm not sure how I should identify this problem. It seems to lean towards being a queing process, M/M/1 and the queue length on average is 20 individuals from 6 a.m to 10.p.m. But I don't know how the customers arrive to the shop but since there should always be 20 customers in the shop then they have to leave with the same rate as they arrive.
Am I supposed to assume that the customers leave right after being served, that is each 3 minutes? I don't know the distribution of any of these times because it's not stated whether the arrival follows a Poisson process or not.
How to go about this?
probability-theory markov-chains queueing-theory
probability-theory markov-chains queueing-theory
asked Jan 11 at 14:17
ParsevalParseval
3,0741719
asked Jan 11 at 14:17
ParsevalParseval
3,0741719
asked Jan 11 at 14:17
ParsevalParseval
3,0741719
asked Jan 11 at 14:17
ParsevalParseval
3,0741719
asked Jan 11 at 14:17
ParsevalParseval
3,0741719
3,0741719
add a comment |
add a comment |
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