Question
In: Statistics and Probability
Customers arrive for service at a rate of 50 an hour and each server can deal...
Customers arrive for service at a rate of 50 an hour and each server can deal with 25 customers an hour. There are three servers. If the customers time is valued at $20 an hour and server time costs $30 an hour, how much does the queue cost for an eight hour day?
Solutions
orchestra answered 2 years agoRelated Solutions
Customers arrive for service at a rate of 50 an hour and each server can deal...
Customers arrive for service at a rate of 50 an hour and each
server can deal with 25 customers an hour. There are three servers.
If the customers time is valued at $20 an hour and server time
costs $30 an hour, how much does the queue cost for an eight hour
day?
Customers arrive at a service facility according to a Poisson process of rate 5 /hour Let...
Customers arrive at a service facility according to a Poisson
process of rate 5 /hour Let N(t) be the number of customers that
have arrived up to time t hours).
a.
What is the probability that there is at least 2 customer walked
in 30 mins?
b.If there was no customer in the first30 minutes, what is the
probability that you have to wait in total of more than 1 hours for
the 1 st customer to show up?
c.For...
Consider three servers. An average of 12 customers per hour arrive from outside at server 1,...
Consider three servers. An average of 12 customers per hour
arrive from outside at server 1, an average of 36 customers per
hour arrive from outside at server 2 and an average of 24 customers
per hour arrive from outside at server 3. Interarrival times are
exponential. Servers 1, 2 and 3 can serve at exponential rates of
100, 120 and 80 customers per hour respectively. After completing
service at server 1, 25% of the customers leave the system and...
Suppose that customers arrive at a bank at a rate of 10 per hour. Assume that...
Suppose that customers arrive at a bank at a rate of 10 per
hour. Assume that the number of customer arrivals X follows a
Poisson distribution.
A. Find the probability of more than 25 people arriving within
the next two hours using the Poisson mass function.
B. Find the probability of more than 25 people arriving within
the next two hours using the normal approximation to the
Poisson.
C. Compute the percent relative difference between the exact
probability computed in...
Customers arrive at a local ATM at an average rate of 14 per hour. Assume the...
Customers arrive at a local ATM at an average rate of 14 per
hour. Assume the time between arrivals follows the exponential
probability distribution. Determine the probability that the next
customer will arrive in the following time frames.
a) What is the probability that the next
customer will arrive within the next 2 minutes?
b) What is the probability that the next
customer will arrive in more than 15 minutes?
c) What is the probability that the next
customer will...
Customers arrive at a two-server system at a Poisson rate λ=5. An arrival finding the system...
Customers arrive at a two-server system at a Poisson rate λ=5.
An arrival finding the system empty is equally likely to enter
service with either server. An arrival finding one customer in the
system will enter service with the idle server. An arrival finding
two others will wait in line for the first free server. The
capacity of the system is 3. All service times are exponential with
rate µ=3, and once a customer is served by either server, he...
Customers arrive at a two-server system according to a Poisson process having rate λ = 5....
Customers arrive at a two-server system according to a Poisson
process having rate λ = 5. An arrival finding server 1 free will
begin service with that server. An arrival finding server 1 busy
and server 2 free will enter service with server 2. An arrival
finding both servers busy goes away. Once a customer is served by
either server, he departs the system. The service times at server i
are exponential with rates μi, where μ1 = 4, μ2...
A bank teller can handle 40 customers an hour and customers arrive every six minutes. What...
A bank teller can handle 40 customers an hour and customers
arrive every six minutes. What is the average time a customer
spends waiting in line?
a. 15 seconds b. 0.40 minutes c. 1.25 minutes d. 30 seconds
Customers arrive at a bakery at an average rate of 18 per hour
on week day mornings. Each clerk can serve a customer in an average
of three minutes. How long does each customer wait in the
system?
a. 1 hour b....
People arrive to a hotel at a rate of 20 on average with each half hour....
People arrive to a hotel at a rate of 20 on average with each half
hour. Make a probability distribution in excel for an interval of
30 minute duration. What’s the probability that no more then 14
customers will arrive?
Customers arrive at a two pump system at Poisson rate two per hour. An arrival finding...
Customers arrive at a two pump system at Poisson rate two per
hour. An arrival finding the system empty is equally likely to
enter service with either pump. An arrival finding one customer in
the system will enter service with the idle pump. An arrival
finding two others in the system will wait in line for the first
free pump. An arrival finding three in the system will not enter.
Two service times are exponential with rates one per hour...
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