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The number of customers arriving at a fast food restaurant are modelled on a Poisson random...
Problem 1. Consider a fast food restaurant where customers arrive and get in line according to...
Problem 1. Consider a fast food restaurant where customers arrive and get in line according to a Poisson process with an average rate of 120 customers per hour. The restaurant has one line and the amount of time it takes the cashier to serve a customer is exponentially distributed with a mean of 2 minutes. Let X_t denote the number of customers in line at time t. 1. Give the state space of the chain (X_t)t≥0. 2. For each state...
7.4 During lunch hour, customers arrive at a fast-food restaurant at the rate of T20 customers...
7.4 During lunch hour, customers arrive at a fast-food restaurant at the rate of T20 customers per hour. The restaurant has one line, with three workers taking food orders at independent service stations. Each worker takes an exponentially dis- tributed amount of time-on average 1 minute-to service a customer. Let X, denote the number of customers in the restaurant (in line and being serviced) at time t. The process (Xt)PO Is a continuous-time Markov chain. Exhibit the generator matrix
3. Customers arrive at the drive-through lane of a fast food restaurant at a rate of...
3. Customers arrive at the drive-through lane of a fast food restaurant at a rate of one every 3 minutes. Use the Poisson probability distribution to answer the following (12 Marks) a. What is the expected number of customers in one hour? b. What is the probability that exactly two customers arriving at the drive-through lane in a nine-minutes interval? c. What is the probability that less than two customers arrive at the drive through lane a nine-minutes interval? d....
The number of customers arriving at a grocery store is a Poisson random Variable with 15...
The number of customers arriving at a grocery store is a Poisson random Variable with 15 On average 10 customers are per hour late the number of customers argon 10am 1 11 What is P(10X1572 O ADAS 8042 C034 D 055
3. A fast food restaurant has a drive-thru window. On average 40 customers arrive at the...
3. A fast food restaurant has a drive-thru window. On average 40 customers arrive at the window every hour. It takes 1 minute on average to serve a customer. a. What is the average number of customers that will be in line and in service at any time? b. On average, how long will a customer spend in the system?
During lunchtime at a certain fast food restaurant, customers arrive at an average rate of 7...
During lunchtime at a certain fast food restaurant, customers arrive at an average rate of 7 customers every 5 minutes. assume a poisson distribution to find the probability that: A) exactly 12 customers arrive in a given 10 minute interval (perform this calculation using an appropriate formula, showing the setup.) b) between 5 and 10 customers (inclusive) arrive in a given 5 minute interval (show how you can answer this from the table) c) after a customer arrives, find the...
The number of drilling rig accidents in a year can be modelled as a Poisson random...
The number of drilling rig accidents in a year can be modelled as a Poisson random variable. Suppose that the expected number of serious accidents per year (for a certain oil company) is λ =5. Find the probability that exactly 2 accidents will happen this year.
In a benchmark study, a fast food restaurant had an average service time of 2.6 minutes....
In a benchmark study, a fast food restaurant had an average service time of 2.6 minutes. Assume that the service time for the fast food restaurant has an exponential distribution. (Round your answers to four decimal places.) (a) What is the probability that a service time is less than or equal to one minute? (b) What is the probability that a service time is between 15 seconds and one minute? (c) Suppose the manager of the restaurant is considering instituting...
In a benchmark study, a fast food restaurant had an average service time of 2.8 minutes....
In a benchmark study, a fast food restaurant had an average service time of 2.8 minutes. Assume that the service time for the fast food restaurant has an exponential distribution. (Round your answers to four decimal places.) (a) What is the probability that a service time is less than or equal to one minute? (b) What is the probability that a service time is between 45 seconds and one minute? (c) Suppose the manager of the restaurant is considering instituting...
Arrivals at a fast-food restaurant follow a Poisson distribution with a mean arrival rate of 16...
Arrivals at a fast-food restaurant follow a Poisson distribution with a mean arrival rate of 16 customers per hour. What is the probability that in the next hour there will be exactly 8 arrivals?
7.4 During lunch hour, customers arrive at a fast-food restaurant at the rate of T20 customers per hour. The restaurant has one line, with three workers taking food orders at independent service stations. Each worker takes an exponentially dis- tributed amount of time-on average 1 minute-to service a customer. Let X, denote the number of customers in the restaurant (in line and being serviced) at time t. The process (Xt)PO Is a continuous-time Markov chain. Exhibit the generator matrix
3. Customers arrive at the drive-through lane of a fast food restaurant at a rate of one every 3 minutes. Use the Poisson probability distribution to answer the following (12 Marks) a. What is the expected number of customers in one hour? b. What is the probability that exactly two customers arriving at the drive-through lane in a nine-minutes interval? c. What is the probability that less than two customers arrive at the drive through lane a nine-minutes interval? d....
The number of customers arriving at a grocery store is a Poisson random Variable with 15 On average 10 customers are per hour late the number of customers argon 10am 1 11 What is P(10X1572 O ADAS 8042 C034 D 055
3. A fast food restaurant has a drive-thru window. On average 40 customers arrive at the window every hour. It takes 1 minute on average to serve a customer. a. What is the average number of customers that will be in line and in service at any time? b. On average, how long will a customer spend in the system?
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