Question

Pete's Market is a small local grocery store with only one checkout counter. Assume that shoppers arrive at the checkout lane according to a Poisson probability distribution, with an arrival rate of 9 customers per hour. The checkout service times follow an exponential probability distribution, with a service rate of 15 customers per hour. The manager's service goal is to limit the waiting time prior to beginning the checkout process to no more than five minutes. Also, the manager of Pete's Market wants to consider one of the following alternatives for improving service. Calculate the value of Wq for each alternative. A. Hire a second person to bag the groceries while the cash register operator is entering the cost data and collecting money from the customer. With this improved single-server operation, the service rate could be increased to 19 customers per hour. Round your answer to three decimal places. Do not round intermediate calculations. Wq= B. Hire a second person to operate a second checkout counter. The two-server operation would have a service rate of 15 customers per hour for each server. Note: Use P0 values from Table 11.4 to answer this question. Round your answer to three decimal places. Do not round intermediate calculations. Wq= 

          Pete's Market is a small local grocery store with only one checkout counter. Assume that shoppers arrive at the checkout lane according to a Poisson probability distribution, with an arrival rate of 9 customers per hour. The checkout service times follow an exponential probability distribution, with a service rate of 15 customers per hour. The manager's service goal is to limit the waiting time prior to beginning the checkout process to no more than five minutes. Also, the manager of Pete's Market wants to consider one of the following alternatives for improving service. Calculate the value of Wq for each alternative.

A. Hire a second person to bag the groceries while the cash register operator is entering the cost data and collecting money from the customer. With this improved single-server operation, the service rate could be increased to 19 customers per hour. Round your answer to three decimal places. Do not round intermediate calculations.
Wq=

B. Hire a second person to operate a second checkout counter. The two-server operation would have a service rate of 15 customers per hour for each server. Note: Use P0 values from Table 11.4 to answer this question. Round your answer to three decimal places. Do not round intermediate calculations.
Wq=
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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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Pete's Market is a small local grocery store with only one checkout counter. Assume that shoppers arrive at the checkout lane according to a Poisson probability distribution, with an arrival rate of 9 customers per hour. The checkout service times follow an exponential probability distribution, with a service rate of 15 customers per hour. The manager's service goal is to limit the waiting time prior to beginning the checkout process to no more than five minutes. Also, the manager of Pete's Market wants to consider one of the following alternatives for improving service. Calculate the value of Wq for each alternative. A. Hire a second person to bag the groceries while the cash register operator is entering the cost data and collecting money from the customer. With this improved single-server operation, the service rate could be increased to 19 customers per hour. Round your answer to three decimal places. Do not round intermediate calculations. Wq= B. Hire a second person to operate a second checkout counter. The two-server operation would have a service rate of 15 customers per hour for each server. Note: Use P0 values from Table 11.4 to answer this question. Round your answer to three decimal places. Do not round intermediate calculations. Wq=
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Pete's Market is a small local grocery store with only one checkout counter. Assume that shoppers arrive at the checkout lane according to a Poisson probability distribution, with an arrival rate of 9 customers per hour. The checkout service times follow an exponential probability distribution, with a service rate of 15 customers per hour. The manager's service goal is to limit the waiting time prior to beginning the checkout process to no more than five minutes. Also, the manager of Pete's Market wants to consider one of the following alternatives for improving service. Calculate the value of Wq for each alternative. A. Hire a second person to bag the groceries while the cash register operator is entering the cost data and collecting money from the customer. With this improved single-server operation, the service rate could be increased to 19 customers per hour. Round your answer to three decimal places. Do not round intermediate calculations. Wq= B. Hire a second person to operate a second checkout counter. The two-server operation would have a service rate of 15 customers per hour for each server. Note: Use P0 values from Table 11.4 to answer this question. Round your answer to three decimal places. Do not round intermediate calculations. Wq=

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Pete's Market is a small local grocery store with only one checkout counter. Assume that shoppers arrive at the checkout lane according to a Poisson probability distribution, with an arrival rate of 18 customers per hour. The checkout service times follow an exponential probability distribution, with a service rate of 20 customers per hour. The manager's service goal is to limit the waiting time prior to beginning the checkout process to no more than five minutes. Also, the manager of Pete's Market wants to consider one of the following alternatives for improving service. Calculate the value of Wq for each alternative. a. Hire a second person to bag the groceries while the cash register operator is entering the cost data and collecting money from the customer. With this improved single-server operation, the service rate could be increased to 28 customers per hour. Round your answer to three decimal places. Do not round intermediate calculations. Wq = _______ minutes b. Hire a second person to operate a second checkout counter. The two-server operation would have a service rate of 20 customers per hour for each server. Note: Use P0 values from Table 11.4 to answer this question. Round your answer to three decimal places. Do not round intermediate calculations. Wq = ____________ minutes

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The Paramount Daily Store has a single checkout stand with a full-time cashier. Customers arrive randomly at the stand at a mean rate of 30 per hour. The service-time distribution is exponential, with a mean of 1.5 minutes. This situation has resulted in occasional long lines and complaints from customers. Therefore, because there is no room for a second checkout stand, the manager is considering the alternative of hiring another person to help the cashier by bagging the groceries. This help would reduce the expected time required to process a customer to 1 minute, but the distribution still would be exponential. The manager would like to have the percentage of time that there are more than two customers at the checkout stand below 25 percent. She also would like to have no more than 5 percent of the customers needing to wait at least 5 minutes before beginning service, or at least 7 minutes before finishing service. Use the formulas for the M/M/1 model to calculate L (system length), Lq (queue length), W (total waiting time in the system), and Wq (waiting time in the queue) P0, P1, and P2 for the current mode of operation. What is the probability of having more than two customers at the checkout stand?

Madhur L.
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Transcript

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00:01 In this question we have been given arrival rate, arrival rate which is denoted by lambda is equal to 9 customers per hour, 9 customers per hour and service rate which is denoted by miao is equal to 15 customers per hour, 15 customers per hour.
00:31 Now we can find the value of lq is equal to lambda square over mu times if mu minus lambda.
00:41 On substituting the values in this we get, we have lambda value is equal to 9, 9 square over 15 times of 15 minus 9.
00:49 And calculating this we get the value of lq is equal to 0 .9.
00:55 This is the required value of lq and from this we can calculate the value of wq is equal to lq over lambda which is equal to 0 .9 over 9.
01:07 So from this we get 0 .1 hars and converting it into minutes we get 0 .1 times of 60 minutes.
01:17 Therefore the value of wq is equal to 6 minutes.
01:22 This is the required solution for part a.
01:26 Now coming to the next part b.
01:29 So here we have lambda is equal to 9 customers per hour, nine customers per hour, and service rate mu is increased to 19 customers per hour.
01:44 So here in the second case, service rate has been increased...
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