In a queueing system, customers arrive once every 4 minutes (standard deviation = 7) and services take 3 minutes (standard deviation = 5.5). (Do not round intermediate calculations. Round your answer to three decimal places.) What is the average time a customer will spend in the queue (in minutes)? minutes
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- In an M/MA queueing system, the arrival rate is 3 customers per hour and the service rate is 5 customers per hour. If the service process is automated (resulting in no variation in service times but the same service rate), what will be the resulting performance measurements? (Round your answers to 3 decimal places.) d. What is the expected number of customers in the queue (Lq)? Number of customers (queue) e. What is the expected waiting time (in hours) in the queue (Na)? Waiting time (queue)Customers enter the camera department of a store at an average rate of six per hour. The department is staffed by one employee, who takes an average of six minutes to serve each arrival. Assume this is a simple Poisson arrival, exponentially distributed service time situation. (Use the Excel spreadsheet Queue Models.) a-1. As a casual observer, how many people would you expect to see in the camera department (excluding the clerk)? Note: Round your answer to 2 decimal places. a-2. How long would a customer expect to spend in the camera department (total time)? Note: Do not round intermediate calculations. Round your answer to the nearest whole number. b. What is the utilization of the clerk? Note: Do not round intermediate calculations. Round your answer to the nearest whole number. c. What is the probability that there are more than two people in the camera department (excluding the clerk)? Note: Round your intermediate calculations to 3 decimal places and final answer to 1…At a fashion retailer, there are three cashiers providing checkout service simultaneously. On average, customers arrive at the checkout area every 6 minutes. It is estimated that the customer arrival process is a Poisson process. The average checkout time for each customer is 12 minutes, with its standard deviation equal to 15 minutes. Suppose that customers form a single line. What is the average waiting time in minutes for a customer? Note: 1. Keep 2 decimal places for your final answer. Either use Excel for your calculation, or keep at least 4 decimal places for your intermediate numbers. 2. The Poisson arrival process has exponentially distributed inter-arrival times.
- At the SuperSpeedy drive-through the time between consecutive customerarrivals has a mean of 50 seconds and a standard deviation of 30 seconds. Thereare two servers whose service time averages 80 seconds with a standard deviationof 20 seconds. Assume that no customers leave the drive-through after entry.b. What is the average time a customer spends at the drive-through? What fractionof that is waiting in the queue?A 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.Consider a base case where a customer arrives every 40 seconds and the Customer Service Champion can handle 120 customers per hour. There are two Food Champions, each capable of handling 100 orders per hour How long should it take to be served by the restaurant (from the time a customer enters the kiosk queue until her food is delivered)? Use queuing models to estimate this.