A vending machine at Municipal Airport dispenses hotcoffee, hot chocolate, or hot tea in a constant service timeof 30 seconds. Customers arrive at the vending machine ata mean rate of 50 per hour, Poisson distributed. Determinethe average length of the waiting line and the average timea customer must wait.

A vending machine at Municipal Airport dispenses hotcoffee, hot chocolate, or hot tea in a constant service timeof 30 seconds. Customers arrive at the vending machine ata mean rate of 50 per hour, Poisson distributed. Determinethe average length of the waiting line and the average timea customer must wait.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section: Chapter Questions

Problem 52P

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Neve Commercial Bank is the only bank in the town of York, Pennsylvania. On a typical Friday, an average of 10 customers per hour arrive at the bank to transact business. There is currently one teller at the bank, and the average time required to transact business if 4 minutes. It is assumed that service times may be described by the negative exponential distribution. If a single teller is used, find: 1. The average time in line 2. The average number in the line 3. The average time in the system 4. The average number in the system 5. The probability that the bank is empty 6. CEO Benjamin Neve is considering a second teller (who would work at the same rate as the first) to reduce waiting time for customers. A single line would be used, and the customer at the front of the line would go to the first available bank teller. He assumes that this will cut the waiting line in half. If the second teller is added, find the new answers to #1 through 6.
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