Problems Queuing Models
 Problems for Queuing Models - Interpret Results

The figure at the left shows a table built by the Queuing Add-In. The arrival and service rates are in units per hour. From the information given, answer the questions below.

 Quantity Value Units Arrival Rate when Empty 5 per hour Service Rate/Channel 2 per hour Number of Channels 2 Max. Number in System *** Type M/M/2/5 Mean Number in System 3.277 units Mean Number in Queue 1.486 units Mean Number in Service 1.791 units Throughput Rate 3.582 units/hour P(0) 0.046 P(1) 0.116 P(2) 0.145 P(3) 0.182 P(4) 0.227 P(5) 0.284 P(6) 0.000

a. Give the meaning of each the symbols M/M given in the “Type” line.

b. What proportion of the arriving customers are not served by this queuing station?

c. For those customers that are served, how long on the average is the time between when they enter the queue and when they leave the service?

d. What is the probability that an arriving customer will wait in the queue?

e. What is the efficiency of the servers?

Operations Research Models and Methods
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by Paul A. Jensen