Question

Work all problems in terms of hours.

1.) If it takes 5 minutes to serve a customer at a fast food restaurant, the service rate is ______ . (Give the number only, don't include any words. )

2.) Customers arrive at a candy shop every 8 minutes on average. What is the arrival rate? (Give the number only.)

3.) In a single-server queuing system, 10 customers arrive per hour, and 20 customers are served per hour. What is the arrival rate?

Answer #1

1,) 12 customers/ hour

In this question, service rate is asked , in order to find it in hours (specifically asked) we will simply divide 60 by 5 minutes which is nothing but conversion.

service rate = 60/5 =12 customers/hour

which means in one hour 12 customers took service.

2.) 7 customers/ hour (approx.)

In this question, arrival rate is asked , in order to find it in hours (specifically asked) we will simply divide 60 by 8 minutes which is nothing but conversion.

service rate = 60/8 =7.5 customers/hour , we can not quantify human beings in fraction therefore here we will take 7 or 8.

which means in one hour 7 0r 8 customers arrive..

likewise in 3.)

3.) 6 customers / hour

A hamburger shop has three competitors. Since people do not like
to wait in long lines for hamburger, the arrival rate to the shop
depends on the number of people in the shop. While n <= 4
customers are present in the shop, customers arrive at a rate of
(20-5n) customers per hour. If more than 4 people are in the shop,
the arrival rate is zero.
For each customer, revenues less raw material costs are 50 cent.
Each server...

A fast-food franchise is considering operating a drive-up window
food-service operation. Assume that customer arrivals follow a
Poisson probability distribution, with an arrival rate of 24 cars
per hour, and that service times follow an exponential probability
distribution. Arriving customers place orders at an intercom
station at the back of the parking lot and then drive to the
service window to pay for and receive their orders. The following
three service alternatives are being considered:
System A: A single-server operation...

During lunch hour, customers arrive at a fast-food restaurant at
the rate of 120 customers per hour. The restaurant has one line,
with three workers taking food orders at independent service
stations. Each worker takes an exponentially distributed amount of
time–on average 1 minute–to service a customer. Let Xt denote the
number of customers in the restaurant (in line and being serviced)
at time t. The process (Xt)t≥0 is a continuous-time Markov chain.
Exhibit the generator matrix.

ANSWER THE FOUR PARTS OR DON'T ANSWER AT
ALL.
Mixed Poisson/exponential
Customers arrive at the drive-up
window of a fast-food restaurant at a rate of 2 per minute during
the lunch hour (12-1pm).
a. What is the probability that exactly 3 customers will arrive
in 1 minute? 1 customer will arrive in 5 minutes?
b. What is the probability that no customers will arrive in 2
minutes?
c. Given a customer has just arrived, what is the probability
that the...

A fast-food franchise is considering operating a drive-up window
food-service operation. Assume that customer arrivals follow a
Poisson probability distribution, with an arrival rate of 25 cars
per hour, and that service times follow an exponential probability
distribution. Arriving customers place orders at an intercom
station at the back of the parking lot and then drive to the
service window to pay for and receive their orders. The following
service alternative is being considered:
System C: A two-server operation with...

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...

Please answer the entire problem!
Problem 15-25 (Algorithmic)
Burger Dome sells hamburgers, cheeseburgers, French fries, soft
drinks, and milk shakes, as well as a limited number of specialty
items and dessert selections. Although Burger Dome would like to
serve each customer immediately, at times more customers arrive
than can be handled by the Burger Dome food service staff. Thus,
customers wait in line to place and receive their orders. Suppose
that Burger Dome analyzed data on customer arrivals and concluded...

Burger Dome sells hamburgers, cheeseburgers, French fries, soft
drinks, and milk shakes, as well as a limited number of specialty
items and dessert selections. Although Burger Dome would like to
serve each customer immediately, at times more customers arrive
than can be handled by the Burger Dome food service staff. Thus,
customers wait in line to place and receive their orders. Suppose
that Burger Dome analyzed data on customer arrivals and concluded
that the arrival rate is 33 customers per...

Problem 15-25 (Algorithmic)
Burger Dome sells hamburgers, cheeseburgers, French fries, soft
drinks, and milk shakes, as well as a limited number of specialty
items and dessert selections. Although Burger Dome would like to
serve each customer immediately, at times more customers arrive
than can be handled by the Burger Dome food service staff. Thus,
customers wait in line to place and receive their orders. Suppose
that Burger Dome analyzed data on customer arrivals and concluded
that the arrival rate is...

An automatic roller coaster ride takes a constant time of 2.5
minutes to complete a ride. Customers arrive at the facility every
2.75 minutes (exponentially distributed). Report answers to 4
decimal places.
a. Determine the average waiting time in the queue (in
minutes).
b. The local bank drive-through teller window can serve a
customer at an average of 4.5 minutes per customer (exponentially
distributed). Customers arrive in their cars at a rate of 12 per
hour (poisson distributed). Determine the...

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