Question

In: Math

Campus Barber Shop has one barber. Customers arrive at a rate of 2.2 per hour, and...

Campus Barber Shop has one barber. Customers arrive at a rate of 2.2 per hour, and haircuts are given at a rate of 3 per hour. Assume the basic Poisson-Exponential model and answer the following questions.

  1. What is the probability that the barber is idle?

  2. What is the probability that one customer is getting a haircut and no one is waiting in the line?

  3. What is the probability that one customer is receiving a haircut and one customer is in the line waiting?

  4. What is the probability that one customer is receiving a haircut and two customers are waiting in the line.

  5. On the average, how many customers are in the shop?

  6. On the average, how long is the line?

  7. What is the average time in the line before service begins.

  8. If a customer arrives at 10:00 AM, when should he expect to leave the shop?


Solutions

Expert Solution


Related Solutions

In a barber, the rate for the number of customers is 3 per hour. On average, the barber can serve customers at a rate of one every 15 minutes.
  In a barber, the rate for the number of customers is 3 per hour. On average, the barber can serve customers at a rate of one every 15 minutes.A)  Find an 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? C)  with which probability that the number of...
Problem 15-9 (Algorithmic) Marty's Barber Shop has one barber. Customers have an arrival rate of 2.1...
Problem 15-9 (Algorithmic) Marty's Barber Shop has one barber. Customers have an arrival rate of 2.1 customers per hour, and haircuts are given with a service rate of 5 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: What is the probability that no units are in the system? If required, round your answer to four decimal places. P0 = What is the probability that one customer is receiving a haircut and no...
Problem 15-9 (Algorithmic) Marty's Barber Shop has one barber. Customers have an arrival rate of 2.1...
Problem 15-9 (Algorithmic) Marty's Barber Shop has one barber. Customers have an arrival rate of 2.1 customers per hour, and haircuts are given with a service rate of 4 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: What is the probability that no units are in the system? If required, round your answer to four decimal places. P0 = ????? What is the probability that one customer is receiving a haircut 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 the rate of 100 per hour. The ticket seller averages 30 seconds per...
Customers arrive at the rate of 100 per hour. The ticket seller averages 30 seconds per customer. What is the average customer time in the system?
Customers arrive at a grocery store at an average of 2.2 per minute. Assume that the...
Customers arrive at a grocery store at an average of 2.2 per minute. Assume that the number of arrivals in a minute follows the Poisson distribution. Provide answers to the following to 3 decimal places. Part a) What is the probability that exactly two customers arrive in a minute? Part b) Find the probability that more than three customers arrive in a two-minute period. Part c) What is the probability that at least seven customers arrive in three minutes, given...
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...
A small auto parts store has a single counter with one employee. Customers arrive at the counter at the rate of 10 per hour according to a Poisson distribution.
 A small auto parts store has a single counter with one employee. Customers arrive at the counter at the rate of 10 per hour according to a Poisson distribution. The employee can handle 20 customers per hour and service times are exponentially distributed. Calculate (A) The probability that a customer finds an empty counter in the auto parts store (no customers waiting or being served) (B) The average number of customers waiting in the que at the auto parts store (i.e.,...
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?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT