"Mega Grocery (MG)" at Atwater operates six checkout counters, each serving its own waiting line. On average, 90 customers per hour are arriving to MG following Poisson distribution. The service time is 3 minutes per customer following exponential distribution. The waiting cost of a customer in the system is $40 per hour. MG is employing one worker at each checkout counter at an hourly wage of $30. Suppose all customers are pooled into a single queue, how many checkout counters would be optimum?

"Mega Grocery (MG)" at Atwater operates six checkout counters, each serving its own waiting line. On average, 90 customers per hour are arriving to MG following Poisson distribution. The service time is 3 minutes per customer following exponential distribution. The waiting cost of a customer in the system is $40 per hour. MG is employing one worker at each checkout counter at an hourly wage of $30. Suppose all customers are pooled into a single queue, how many checkout counters would be optimum?

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Description: "Mega Grocery (MG)" at Atwater operates six checkout counters, each serving itsown waiting line. On average, 90 customers per hour are arriving to MG followingPoisson distribution. The service time is 3 minutes per customer followingexponential dist

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Vehicles arrive at a car detailing service at a rate of 10 per minute according to a Poissondistribution. For simplicity, assume that there is only one lane and one worker who can serve atan average rate of 12 vehicles per minute. Service times are exponentially distributed. Part A: What is the average length of the queue? Part B: What is the average time a vehicle must spend to get through the system? Part C: What is the utilization rate of the worker? Part D: What is the probability that when you arrive at the shop, there will be three ormore vehicles ahead of you?
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Question 4 Multi-Server QueueA supermarket manager is trying to decide how many cashers to employ for the peak time. The service times for check outs are exponentially distributed with a mean service time of 3 minutes. Customer arrivals to cashiers follow a Poisson arrival process with an average 110 customers per hour.a. What is the minimum number of cashers that would be needed to have the utilization less than one?b. If the waiting time is too long, customers might leave the store or even do not enter the store. It is estimated that for every minute of waiting time, the supermarket loses a potential profit of 50 HKD every hour from lost sales. The hourly wage for a casher is 80 HKD / hour. How many cashers should the supermarket employ to maximize its profit? (Keep four decimal places.