Analysis of arrivals to a single pump gas station has shown that the times between arrivals...
Analysis of arrivals to a single pump gas station has shown that the times between arrivals can be depicted by negative exponential distribution with a mean of 10 minutes. Service times were observed to be distributed negative exponentially, as well, with a mean time of 6 minutes. What is the steady-state mean number of customers at the station and the steady-state mean number that are waiting?
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Analysis of arrivals to a single pump gas station has shown that
the times between arrivals...
QUESTION 2: Consider a check–out station at a small store with customer arrivals described by a...
QUESTION 2:
Consider a check–out station at a small store with customer
arrivals described by a Poisson process with intensity ? = 10
customers per hour. There are two service team members, Tom and
Jerry, working one per shift. In Tom’s shift, the service times are
exponentially distributed with the mean time equal to 3 minutes,
while for Jerry service times are exponentially distributed with
the mean time equal to 5 minutes.
1. Find the mean queue length during the...
Question 2 Individual customers arrive at a gas station randomly. The time of each arrival Tn has the following probability density function: fTa (t) There are c pumps. The time it takes to fill a ga...
Question 2 Individual customers arrive at a gas station randomly. The time of each arrival Tn has the following probability density function: fTa (t) There are c pumps. The time it takes to fill a gas tank at a particular pump is exponentially distributed with mean џ. Pumping times are independent Find the stationary distribution of the number of customers at the gas station (waiting for a pump, or pumping). Assume λ. Simplify the result as much as possible (no...
Question 2 Individual customers arrive at a gas station randomly. The time of each arrival Tn has the following probability density function: fTa (t) There are c pumps. The time it takes to fill a ga...
Question 2 Individual customers arrive at a gas station randomly. The time of each arrival Tn has the following probability density function: fTa (t) There are c pumps. The time it takes to fill a gas tank at a particular pump is exponentially distributed with mean џ. Pumping times are independent Find the stationary distribution of the number of customers at the gas station (waiting for a pump, or pumping). Assume λ. Simplify the result as much as possible (no...
Question 2 Individual customers arrive at a gas station randomly. The time of each arrival Tn has the following probability density function: fTa (t) There are c pumps. The time it takes to fill a ga...
Question 2 Individual customers arrive at a gas station randomly. The time of each arrival Tn has the following probability density function: fTa (t) There are c pumps. The time it takes to fill a gas tank at a particular pump is exponentially distributed with mean џ. Pumping times are independent Find the stationary distribution of the number of customers at the gas station (waiting for a pump, or pumping). Assume λ. Simplify the result as much as possible (no...
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...
10. The times between train arrivals at a certain train station is exponentially distributed with a...
10. The times between train arrivals at a certain train station is exponentially distributed with a mean of 10 minutes. I arrived at the station while Dayer was already waiting for the train. If Dayer had already spent 8 minutes before I arrived, determine the following a. b. c· The average length of time I will wait until the next train arrives The probability that I will wait more than 5 minutes until the next train arrives The probability that...
Problem 5: 10 points Consider a service station with N- 8 servers. Customer arrivals form a...
Problem 5: 10 points Consider a service station with N- 8 servers. Customer arrivals form a Poisson process with the rate ? = 7 per hour. However, if there is a vacant seat (that is if the number of customers ongoing their services is n S 7, then the new customer begins the service. However, if n 8, the new customer leaves the system Individual service times are independent exponentially distributed with the mean t o20 minutes. 1. Describe the...
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...
subject: operations research When customers arrive at Cool's Ice Cream Shop, they take a number and...
subject: operations research When customers arrive at Cool's Ice Cream Shop, they take a number and wait to be called to purchase ice cream from one of the counter servers. From experience in past summers, the store's staff knows that customers arrive at a rate of 150 per hour on summer days between 3:00 p.m. and 10:00 p.m., and a server can serve 1 customer in 1 minute on average. Cool's wants to make sure that customers wait no longer...
A single server waiting line system has an arrival pattern characterized by a Poisson distribution with...
A single server waiting line system has an arrival pattern characterized by a Poisson distribution with 3 customers per hour. The average service times is 12 minutes. the service times are distributed according to the negative exponential distribution. The expected number of customers in the system is : A) 3.0 B) 1.5 C) 1.0 D) .90 The expected number of customers waiting in line is: A) 6 B) 7 C) 8 D) 9 Please show work
QUESTION 2:
Consider a check–out station at a small store with customer
arrivals described by a Poisson process with intensity ? = 10
customers per hour. There are two service team members, Tom and
Jerry, working one per shift. In Tom’s shift, the service times are
exponentially distributed with the mean time equal to 3 minutes,
while for Jerry service times are exponentially distributed with
the mean time equal to 5 minutes.
1. Find the mean queue length during the...
Question 2 Individual customers arrive at a gas station randomly. The time of each arrival Tn has the following probability density function: fTa (t) There are c pumps. The time it takes to fill a gas tank at a particular pump is exponentially distributed with mean џ. Pumping times are independent Find the stationary distribution of the number of customers at the gas station (waiting for a pump, or pumping). Assume λ. Simplify the result as much as possible (no...
Question 2 Individual customers arrive at a gas station randomly. The time of each arrival Tn has the following probability density function: fTa (t) There are c pumps. The time it takes to fill a gas tank at a particular pump is exponentially distributed with mean џ. Pumping times are independent Find the stationary distribution of the number of customers at the gas station (waiting for a pump, or pumping). Assume λ. Simplify the result as much as possible (no...
Question 2 Individual customers arrive at a gas station randomly. The time of each arrival Tn has the following probability density function: fTa (t) There are c pumps. The time it takes to fill a gas tank at a particular pump is exponentially distributed with mean џ. Pumping times are independent Find the stationary distribution of the number of customers at the gas station (waiting for a pump, or pumping). Assume λ. Simplify the result as much as possible (no...
10. The times between train arrivals at a certain train station is exponentially distributed with a mean of 10 minutes. I arrived at the station while Dayer was already waiting for the train. If Dayer had already spent 8 minutes before I arrived, determine the following a. b. c· The average length of time I will wait until the next train arrives The probability that I will wait more than 5 minutes until the next train arrives The probability that...
Problem 5: 10 points Consider a service station with N- 8 servers. Customer arrivals form a Poisson process with the rate ? = 7 per hour. However, if there is a vacant seat (that is if the number of customers ongoing their services is n S 7, then the new customer begins the service. However, if n 8, the new customer leaves the system Individual service times are independent exponentially distributed with the mean t o20 minutes. 1. Describe the...
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...
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