A service counter employs two servers. On average a server requires 8 minutes to process a customer and service times follow an exponential distribution. Customers arrive at the counter at the rate of 12 per hour according to a Poisson distribution. The service rate per server for this system is
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- Please do not give solution in image formate thanku. λ= 4 customers per hour; μ = 5 customers per hour; M= 1 An average of 20 customers arrive at a service center each hour. There are two servers on duty, and each can process 12 customers per hour. a) What is the system utilization? b) What is the average waiting time for customers who actually have to wait? c) What is the average time customers wait in line for service?A vending machine dispenses hot chocolate or coffee. Service time is 35 seconds per cup and is constant. Customers arrive at a mean rate of 66 per hour, and this rate is Poisson-distributed. a. Determine the average number of customers waiting in line. (Round your answer to 2 decimal places.) Average number of customers ?? b. Determine the average time customers spend in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average time minutes ??You observe an average of 10 customers in the System. On average, you also observe customers are in the system for 50 minutes before they leave. What is the arrival rate into the system in customers per hour?
- A vending machine dispenses hot chocolate or coffee. Service time is 15 seconds per cup and is constant. Customers arrive at a mean rate of 55 per hour, and this rate is Poisson-distributed. a. Determine the average number of customers waiting in line. (Round your answer to 2 decimal places.) Average number of customer b. Determine the average time customers spend in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average time minutes c. Determine the average number of customers in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.)A vending machine dispenses hot chocolate or coffee. Service time is 30 seconds per cup andis constant. Customers arrive at a mean rate of 80 per hour, and this rate is Poissondistributed.A) Identify the Queuing Model and sketch the system.B) What is the arrival rate?C) What is the service rate?A vending machine dispenses hot chocolate or coffee. Service time is 45 seconds per cup and is constant. Customers arrive at a mean rate of 59 per hour, and this rate is Poisson-distributed. a. Determine the average number of customers waiting in line. (Round your answer to 2 decimal places.) Average number of customer b. Determine the average time customers spend in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average time minutes c. Determine the average number of customers in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average number customers
- Repair calls are handled by one repairman at a photocopy shop. Repair time, including traveltime, is exponentially distributed, with a mean of two hours per call. Requests for copierrepairs come in at a mean rate of three per eight-hour day (assume Poisson).A) Identify the Queuing Model and sketch the system.B) What is the arrival rate?C) What is the service rate?D) What is the average number of customers awaiting repairs?λ = 3 Customers per hour μ = 5 Customers per hour M = 1 (a) What is the system utilization? (b) What is the average number of customers waiting for service? (c) What is the average time customers wait in line for service?During the early morning hours, customers arrive at a branch post office at an average rate of 45 per hour (Poisson), while clerks can handle transactions in an average time (exponential) of 4 minutes each. Find: (a) The average number of customers waiting for service if 5 clerks are used. (b) The minimum number of clerks needed to keep the average waiting time in the system to under 5 minutes. (c) If clerk cost is $40 per hour and customer waiting time represents a “cost” of $30 per hour, how many clerks can be justified on a cost basis? Please show work.
- A small town with one hospital has 4 ambulances to supply ambulance service. Requests for ambulances during nonholiday weekends average 0.72 per hour and tend to be Poisson-distributed. Travel and assistance time averages 2.60 hours per call and follows an exponential distribution Use Table 18.4. a. Find system utilization. (Round your answer to the nearest whole percent.) System utilization b. Find the average number of customers waiting. (Round your answer to 3 decimal places.) Average number of customers c. Find the average time customers wait for an ambulance. (Round your answer to 3 decimal places.) Average time hourA server operates with 90 % utilization. Coefficient of variation of service process is 0.6. Coefficient of variation of arrival process is 0.8. Average processing time is 4 minutes. What is the average time a customer spends in the system using the single server queuing model ? Show all formulas used, calculations and results.Ali Baba‘s Car Wash Service Centre is open 6 days a week, but its busiest day isalways on Sunday. From the previous data, Ali Baba estimates that dirty carsarrive at the rate of one every two minutes. One car at a time is cleaned in thisexample of a single-channel waiting line. Assuming Poisson arrivals andexponential service times, find the following: a.Compute the average number of cars in line. b.Calculate the value of probability that there are no car in the system. c.Compute the average time that a car spends in the system.