Question

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 and in the system? (2 points)

Recently, Joe has started receiving complaints regarding long waiting time from customers who want faster service. In response, Joe is considering hiring Jim to work with him at the stand. Assume that Jim can also serve customers at the same rate as Joe. Compute the average time that a customer spends waiting in the queue and in the system for the following cases:

c) There is a single queue at the stand for both servers. (2 points)

d) There are two queues at the stand, each operating independently, and customers are served FCFS within each queue. Assume that the average arrival rate to each queue is half of that in the previous case, i.e., 49/2, and follows a Poisson distribution. (2 points)

e) From a customer’s perspective, which system is better in terms of waiting time in the system (a shared queue for the two servers as in Part c or dedicated queues for each server as in Part d?

Answer #1

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...

Burger house sells hamburgers, cheeseburgers, French fries, soft
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
that the arrival rate is 45 customers per hour...

6. Consider a queueing system having two servers and no queue.
There are two types of customers. Type 1 customers arrive according
to a Poisson process having rate ??, and will enter the system if
either server is free. The service time of a type 1 customer is
exponential with rate ??. Type 2 customers arrive according to a
Poisson process having rate ??. A type 2 customer requires the
simultaneous use of both servers; hence, a type 2 arrival...

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...

Customers arrive to a single server system in accordance with a
Poisson pro- cess with rate λ. Arrivals only enter if the server is
free. Each customer is either a type 1 customer with probability p
or a type 2 customer with probabil- ity 1 − p. The time it takes to
serve a type i customer is exponential with rate μi , i = 1, 2.
Find the average amount of time an entering customer spends in the
system.

1.) A system has 5 servers. Customers arrive at a rate of 6 per
hour and service time is 20 minutes. What is the service rate of
the system?
2.) A system has 5 servers. Customers arrive at a rate of 6 per
hour and service time is 20 minutes. What is the system
utilization? (Show answer as a decimal.)
3.)Suppose that this system has 3 servers instead of 5. What is
the probability there are no customers in the...

Customers arrive at coffee shop at a rate of 40 per hour. There
are 2 servers available and it takes an average of 1 minute to
serve each customer.
Using Table 12-6, what is the probability of no customers in the
system?
0.333
0.5
0.667
0

n a barber the rate for the number of the customers is 3 per
hours. On an average the barber can serve customers at rate of one
every 15 minutes.
A) Find average number of the customers in the
barber (system) and queue?
B) Find average waiting time in the barber and
queue?
C) What is the probability that the barber be
empty?
D) What is the probability that exactly 2 customers
present in the system

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