According to queuing theory, what percentage of the time will the receiving admi

Question

According to queuing theory, what percentage of the time will the receiving administrator be busy? What is the average number of jobs being actively worked on in this area?

The receiving area is staffed by a single administrator, who can handle 0.80 jobs per hour, with service times being negative exponentially distributed. In addition, assume that the inter-arrival times for jobs are negative exponentially distributed.

Work day 8 hours I- 12.32 Standard CAD Jobs 50% I 6.54 I1.67 2590 Complex CAD Jobs 100% , +| Receiving 0.5 jobs per hour R 2590 Rejected Customer declines

Explanation / Answer

This is M/M/1 queue model

Arrival rate, ? = 0.5 jobs per hour

Service rate, ? = 0.8 jobs per hour

According to queuing theory,

Percentage of time, the receiving administrator will be busy = ?/? = 0.5/0.8 = 0.625 or 62.5 %

Average number of jobs being actively worked on in the receiving area, Iq = I - ?/? = 1.67 - 0.5/0.8 = 1.0417

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