Problem 11-13 (Algorithmic)

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 12 customers per hour. The checkout service times follow an exponential probability distribution, with a service rate of 16 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 W_q 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 28 customers per hour. Round your answer to three decimal places. Do not round intermediate calculations. W_q = 1.607 minutes

TABLE 11.4 VALUES OF P, FOR MULTIPLE-SERVER WAITING LINES WITH POISSON ARRIVALS AND EXPONENTIAL SERVICE TIMES Number of Servers () Ratio A/ 2 3 4 5 0.15 0.8605 0.8607 0.8607 0.8607 0.20 0.8182 0.8187 0.8187 0.8187 0.25 0.7778 0.7788 0.7788 0.7788 0.30 0.7391 0.7407 0.7408 0.7408 0.35 0.7021 0.7046 0.7047 0.7047 0.40 0.6667 0.6701 0.6703 0.6703 0.45 0.6327 0.6373 0.6376 0.6376 0.50 0.6000 0.6061 0.6065 0.6065 0.55 0.5686 0.5763 0.5769 0.5769 0.60 0.5385 0.5479 0.5487 0.5488 0.65 0.5094 0.5209 0.5219 0.5220 0.70 0.4815 0.4952 0.4965 0.4966 0.75 0.4545 0.4706 0.4722 0.4724 0.80 0.4286 0.4472 0.4491 0.4493 0.85 0.4035 0.4248 0.4271 0.4274 0.90 0.3793 0.4035 0.4062 0.4065 0.95 0.3559 0.3831 0.3863 0.3867 1.00 0.3333 0.3636 0.3673 0.3678 1.20 0.2500 0.2941 0.3002 0.3011 1.40 0.1765 0.2360 0.2449 0.2463 1.60 0.1111 0.1872 0.1993 0.2014 1.80 0.0526 0.1460 0.1616 0.1646 2.00 0.1111 0.1304 0.1343 2.20 0.08 15 0.1046 0.1094 2.40 0.0562 0.0831 0.0889 2.60 0.0345 0.0651 0.0721 2.80 0.0160 0.0521 0.0581 3.00 0.0377 0.0466 3.20 0.0273 0.0372 3.40 0.0186 0.0293 3.60 0.0113 0.0228 3.80 0.0051 0.0174 4.00 0.0130 4.20 0.0093 4.40 0.0063 4.60 0.0038 4.80 0.0017