A social security Administration branch is considering the following two options for processing applications for social security cards. Option 1: Three clerks process applications in parallel from a single queue. Each clerk fills out the form for the application in the presence of the applicant. Processing time is exponential with a mean of 15 minutes. Ineterarrival times are exponential. Option 2: Each applicant first fills out an application wit

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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A social security Administration branch is considering the following two options for processing
applications for social security cards.
Option 1: Three clerks process applications in parallel from a single queue. Each clerk fills out
the form for the application in the presence of the applicant. Processing time is exponential
with a mean of 15 minutes. Ineterarrival times are exponential.
Option 2: Each applicant first fills out an application with-out the clerk’s help. The time to
accomplish this is exponentially distributed, with a mean of 65 minutes. When the applicant
has filled out the form, he or she joins a single line to wait for one of the three clerks to check
the form it takes a clerk an average of 4 minutes ( exponentially distributed) to review the
application
The interarrival times of applicants is exponential, and average of 4.8 customers arrive each
hour. Which option will get applicants out of the office more quickly. 

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