Customers arrive at a video rental desk at the rate of one per minute (exponential interarrival times). Each server can handle 04 customers per minute (exponential service times). If there are 4 servers, what is the probability of three or fewer customers in the system?
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please answer this for my review
Given that,
Clients show up at a pace of one every moment. That is,
The server can deal with 0.4 clients each moment. That is,
The quantity of servers is 4. That is,
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- Customers arrive at Best-Bank-in-Town’s (BBT) sole ATM location at a rate of 21 customers per hour. It is assumed that the arrival process is random. BBT recently hired an intern who estimated that the average service time is 2 minutes per customer with a standard deviation of 1.2 minutes. [Assume that the arrival rate is the same throughout the day without peak and off-peak considerations and that there is only one ATM machine at that location] 1. Calculate average waiting time for ATM user at the BBT location 2. Calculate average length of queue at the ATM location (i.e. average numbers of customers waiting for service)? 3. What is the probability that an arriving customer has no waiting time to use the ATM? 4. BBT wants to cut the average waiting time in half without necessarily adding another ATM machine. They are in discussions with their ATM software provider who has told them that their new software is very consistent with information retrieval and can greatly minimize the…People arrive randomly at a bank teller at an average rate of 20 an hour. If the teller takes an average of 1 minute to serve each customer, what is the average number of people in the systemPatients arrive at a dentist’s office with an arrival rate of 2.8 patients per hour. The dentist can treat patients at a service rate of 3 patients per hour. A study of patient waiting times shows that a patient waits an average of 30 minutes before seeing the dentist. Note the M/M/1 model does not necessarily apply here. What are the arrival and service rates in terms of patients per minute? What is the average number of patients in the waiting room? If a patient arrives at 10:10am, at what time is the patient expected to leave the office?
- At a particular service operation, customers form a single queue that operates on a first-come, first-served basis. There is one server. Customers arrive at the rate of 12 per hour. Using the current technology in place, the server can process 15 customers per hour. Upgrades to the technology, as listed below, would allow the server capacity to increase. For example, an expenditure of $1,000 would allow the server to process 16 customers per hour. The manager wishes to insure that the time the average customer must spend in the system is less than or equal to 10 minutes. What is the minimum amount of money the manager must spend on technology to meet that standard? $1,000 service is 16 customers per hour $3,000 service is 17 customers per hour $5,000 service is 18 customers per hour $7,000 service is 20 customers per hour $10,000 service is 22 customers per hour…Customers arrive at a server queuing system according to a Poisson process with mean rate of 30 per hour. If the server works continuously, the number of customers it can serve in an hour has Poisson distribution with mean 50. } Determine the proportion of the time during which no one waits for service.Consider a bank with two tellers. An average of 2 customers per hour arrive at the bank and wait in a single línea for an idle teller. The average time it takes to serve a customer is triangular (x1=1, y1=0), (x2=4, y2=2/3) Assume that inter-arrival times and services time is exponential. Develop the service (ST) equation? a. Y=2x-22/6B. Y=2x-22/3C. Y=22/3x-2/3D. Y=2x-3/22