Question

*please use excel and provide the formulas

Customers arrive randomly at a product returns counter at a department store, which meets the assumptions of the Single-Server, Single-Phase waiting line model (i.e., the arrival rate is Poisson distributed and service rate is exponentially distributed). There is only one returns employee, and the time required for returns varies from customer to customer. There is a single waiting line. The average arrival rate is 15 customers per hour. The average time to serve a customer is 2.25 minutes. Respond to the following questions: a. What is the utilization factor? b. How long can a customer expect to wait in line? c. How many customers are expected to wait to be serviced? d. How many customers are expected to be in the system? e. How long can a customer expect to wait to be serviced and be serviced? f. What is the probability that there are exactly 2 customers in the system? g. What is the probability that there are exactly 4 customers in the system?

Answer #1

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In a grocery store, there is one cashier counter. Customers
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arrival rate is 30 customers per hour. The service time is
exponentially distributed. The mean service time is 1 minute 30
seconds.
1. What is the expected number of customers waiting in the
system.
2. What is the expected waiting time.( unit in minutes)
3. What is the utilization rate (unit in %) of
the cashier?

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Suppose that the customers arrive at a hamburger stand at an
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service time is exponentially distributed.
a) What is the average number of people waiting in queue and in
the system? (2 points)
b) What is the average time that a customer spends waiting in
the queue...

Suppose that the customers arrive at a hamburger stand at an
average rate of 49 per hour, and the arrivals follow a Poisson
distribution. Joe, the stand owner, works alone and takes an
average of 0.857 minutes to serve one customer. Assume that the
service time is exponentially distributed.
a) What is the average number of people waiting in queue and in
the system? (2 points)
b) What is the average time that a customer spends waiting in
the queue...

Please answer the entire problem!
Problem 15-25 (Algorithmic)
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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...

1.1 (M/M/1) model - use the qtsPlus or other software to answer
the questions. In a grocery store, there is one cashier. Customers
arrive at the cashier counter according to a Poisson process. The
arrival rate is 18 customers per an hour. Customers are served in
order of arrival (FCFS: first come first service). The service time
(i.e. the time needed for scanning the items and processing
payment) is exponentially distributed. The mean service time is 3
minutes. A) Once...

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drinks, and milkshakes, as well as a limited number of specialty
items and dessert selections. Although Burger house would like to
serve each customer immediately, at times more customers arrive
than can be handled by the Burger house food service staff. Thus,
customers wait in line to place and receive their orders. Suppose
that Burger house analyzed data on customer arrivals and concluded
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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...

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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
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