A car wash has one automatic car wash machine. Cars arrive according to a Poisson process...
A car wash has one automatic car wash machine. Cars arrive according to a Poisson process at an average rate of 5 every 30 minutes. The car wash machine can serve customers according to a Poisson distribution with a mean of 0.25 cars per minute. What is the probability that there is no car waiting to be served?
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A car wash has one automatic car wash machine. Cars arrive
according to a Poisson process...
Star Car Wash estimates that dirty cars arrive at the rate of 15 per hour all...
Star Car Wash estimates that dirty cars arrive at the rate of 15 per hour all day and at the wash line, the cars can be cleaned at the rate of one every 4 minutes. One car at a time is cleaned in this example of a single-channel waiting line. Assuming Poisson arrivals and exponential service times, find the: (a) average time a car spends in the service system. (b) average number of cars in line. (c) average time a...
Assume that for a gas and car wash station one car can be serviced at a...
Assume that for a gas and car wash station one car can be serviced at a time. The arrivals follow a Poisson probability distribution, with an arrival rate of 1 car every 10 minutes and the service times follow an exponential probability distribution, with a service rate of 8 cars per hour. What is the probability that the station will be idle? What is the average number of cars that will be waiting for service? What is the average time...
Suppose that vehicles arrive at a car wash following a Poisson process with an average of...
Suppose that vehicles arrive at a car wash following a Poisson process with an average of 12 cars per hour. What is the probability that it takes less than 2 hours for 20 cars to arrive?
Problem 4. The Security & Trust Bank employs 4 tellers to serve its customers. Customers arrive a...
Problem 4. The Security & Trust Bank employs 4 tellers to serve its customers. Customers arrive ac cording to a Poisson process at a mean rate of 4 per minute. However, business is growing and management projects that the mean arrival rate will be 6 per minute a year from now. The transaction time between the teller and customer has an exponential distribution with a mean of 0.5 minute. Management has established the following guidelines for a satis- factory level...
Customers arrive at a service facility with one server according to a Poisson process with a...
Customers arrive at a service facility with one server according to a Poisson process with a rate of 5 per hour. The service time are i.i.d. exponential r.v.´s, and on the average, the server can serve 7 customers per hour. Suppose that the system is in the stationary regime. (a) What is the probability that at a particular time moment, there will be no queue? (b) What is the probability that a particular time moment, there will be more than...
QUESTION 1 Customers arrive at a hair salon according to a Poisson process with an average of 1...
QUESTION 1 Customers arrive at a hair salon according to a Poisson process with an average of 16 customers per hour. Which of the following is most likely true, based on this information: a. The hair salon serves customers on a walk-in basis (rather than by appointment times) b. If 10 customers arrive in the first hour, it is likely that 22 customers will arrive in the next hour. c. If the salon can serve an average of 20 customers...
175-5.* A service station has one gasoline pump. Cars wanting gasoline arrive according to a Poisson...
175-5.* A service station has one gasoline pump. Cars wanting gasoline arrive according to a Poisson process at a mean rate of 15 per hour. However, if the pump already is heing used, these po- tential customers may balk (drive on to another service station). In particular, if there are n cars already at the service station, the prob- ability that an arriving potential customer will balk is n/3 for n 1. 2, 3. The time required to service a...
Problem 6. Janet is planning to open a small two-bay car-wash operation, and she must decide...
Problem 6. Janet is planning to open a small two-bay car-wash operation, and she must decide how much space to provide for waiting cars. Janet estimates that customers would arrive ran- domly (i.e., a Poisson input process) with a mean rate of 1 every 4 minutes, unless the waiting area is full, in which case the arriving customers would take their cars elsewhere. The time that can be attributed to washing one car has an exponential distribution with a mean...
Problem 4. Marsha operates an expresso stand. Customers arrive according to a Poisson process at ...
Problem 4. Marsha operates an expresso stand. Customers arrive according to a Poisson process at a mean rate of 30 per hour. The time needed by Marsha to serve a customer has an exponential distribution with a mean of 90 seconds (a) Find L, Lq, W, and W (b) Suppose Marsha is replaced by an expresso vending machine that requires exactly 75 seconds for each customer to operate. Find L, Lq, W, and W
Problem 4. Marsha operates an expresso...
Please answer using stochastic operations principles Cars arrive at a rate of 10 per hour in a single-server drive-in restaurant. Assume that the teller serves vehicles with a rate exponentially distr...
Please answer using stochastic
operations principles
Cars arrive at a rate of 10 per hour in a single-server drive-in restaurant. Assume that the teller serves vehicles with a rate exponentially distributed with a mean of 4 minutes per car (ie, a rate of 1 car every 4 minutes). Answer the following questions: (a) What is the probability that the teller is idle? (b) What is the average number of cars waiting in line for the teller? (A car that is...
Problem 4. The Security & Trust Bank employs 4 tellers to serve its customers. Customers arrive ac cording to a Poisson process at a mean rate of 4 per minute. However, business is growing and management projects that the mean arrival rate will be 6 per minute a year from now. The transaction time between the teller and customer has an exponential distribution with a mean of 0.5 minute. Management has established the following guidelines for a satis- factory level...
175-5.* A service station has one gasoline pump. Cars wanting gasoline arrive according to a Poisson process at a mean rate of 15 per hour. However, if the pump already is heing used, these po- tential customers may balk (drive on to another service station). In particular, if there are n cars already at the service station, the prob- ability that an arriving potential customer will balk is n/3 for n 1. 2, 3. The time required to service a...
Problem 6. Janet is planning to open a small two-bay car-wash operation, and she must decide how much space to provide for waiting cars. Janet estimates that customers would arrive ran- domly (i.e., a Poisson input process) with a mean rate of 1 every 4 minutes, unless the waiting area is full, in which case the arriving customers would take their cars elsewhere. The time that can be attributed to washing one car has an exponential distribution with a mean...
Problem 4. Marsha operates an expresso stand. Customers arrive according to a Poisson process at a mean rate of 30 per hour. The time needed by Marsha to serve a customer has an exponential distribution with a mean of 90 seconds (a) Find L, Lq, W, and W (b) Suppose Marsha is replaced by an expresso vending machine that requires exactly 75 seconds for each customer to operate. Find L, Lq, W, and W
Problem 4. Marsha operates an expresso...
Please answer using stochastic
operations principles
Cars arrive at a rate of 10 per hour in a single-server drive-in restaurant. Assume that the teller serves vehicles with a rate exponentially distributed with a mean of 4 minutes per car (ie, a rate of 1 car every 4 minutes). Answer the following questions: (a) What is the probability that the teller is idle? (b) What is the average number of cars waiting in line for the teller? (A car that is...
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