Question

In: Statistics and Probability

Pete's Market is a small local grocery store with only one checkout counter. Assume that shoppers...

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 13 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.

  1. 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 29 customers per hour. Round your answer to three decimal places. Do not round intermediate calculations
  2. 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.

Solutions

Expert Solution

a) this is M/M/1 system

lambda = 13 /hour

mu = 29/hour

Wq = 0.028 hour

b)

this is M/M/2 queue

here mu = 20 per hour

c = 2

Wq = 0.0059 hours

orchestra answered 1 year ago
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