You are reviewing a simulation model and find that the analyst who prepared the model used generate the waiting time at a restaurant (in seconds). Which of the following assumptions did the analyst make about the waiting time? I. The minimum waiting time is 100. II. The average (mean) waiting time is 100. II. The waiting time is normally distributed.
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- Which of the following is a qualitative factor in a simulation of a grocery store checkout process? A. the interarrival time of customers to the queue B.the number of full-service checkout lanes that are open C. the number of express lanes that are open D. the presence of self-checkout lanes10. Two operators handle adjustments for a group of 10 machines. Adjustment time is exponentiallydistributed and has a mean of 14 minutes per machine. The machines operate for an average of86 minutes between adjustments. While running, each machine can turn out 50 pieces per hour.Find the following:a. The probability that a machine will have to wait for an adjustmentb. The average number of machines waiting for adjustmentc. The average number of machines being servicedd. The expected hourly output of each machine, taking adjustments into accounte. Machine downtime represents a cost of $70 per hour; operator cost (including salary andfringe benefits) is $15 per hour. What is the optimum number of operators?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?
- Calls arrive at Lynn Ann Fish's hotel switchboard at a rate of 2.0 per minute. The average time to handle each is 15 seconds. There is only one switchboard operator at the current time. The Poisson and negative exponential distributions appear to be relevant in this situation. a) The probability that the operator is busy = 0.500.50 (round your response to two decimal places). b) The average time that a caller must wait before reaching the operator = 0.250.25 minutes (round your response to two decimal places). c) The average number of calls waiting to be answered = nothing calls (round your response to two decimal places).Consider a bank where potential customers arrive at rate of 60 customers per hour. However, because of limited space, one out of every four arriving customers finds the bank full and leaves immediately (without enteringthe bank). Suppose that the average number of customers waiting in line in the bank is 3.5. How long will a typical entering customer have to wait in line? (Hint: In Little’s formula, l refers only to customers who enter the system.)A radio repairer notes that the time he spends on his job has an exponential distribution with a mean of 4 minutes. He follows the first come first serve principle. The arrival time of clients takes a Poisson distribution with an average rate of 8 clients every 1 hour.Determine the arrival rate value , service rate value to be used,time taken by aclient waiting in the queue Determine the client’s average waiting time in the system and Compute the probability that the system is idle; P (idle)
- Given the following Operating Characteristics from a queuing model with time units specified in hours, answer the five questions: Po = 0.4000 Lq = 0.9000 L = 1.5000 Wq = 0.2000 W = 0.3000 Pw = 0.6000 What is the average time, in minutes, a customer waits in line before being served? What is the average time, in minutes, a customer spends waiting and being served? What is the average number of customers in the system? What is the probability that there are no customers in the system? If the system serves a customer every 4 minutes, what is the service rate?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)Suppose the waiting time at a certain checkout counter is bi-modal. With probability 0.85, the waiting time follows an exponential distribution with a mean waiting time of four minutes. With probability 0.15, the waiting time equals 20 minutes. a) Compute the mean and median waiting time at the checkout counter. b) Compute the variance of the waiting time at the checkout counter. c) Compute the probability that an individual customer waits longer than 5 minutes at the checkout counter.
- One operator loads and unloads a group of five machines. Service time is exponentiallydistributed with a mean of 10 minutes per cycle. Machines run for an average of 70 minutesbetween loading and unloading, and this time is also exponential. Find the following:a. The average number of machines waiting for the operatorb. The expected number of machines runningc. Average downtimed. The probability that a machine will not have to wait for serviceAt 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.