aBbCel AaBbCc AaBbCeD AaBbCeD AaBbCeD AaBboD AaBbcc AaB AaBbce 1 Body Text 1 Hea

Question

aBbCel AaBbCc AaBbCeD AaBbCeD AaBbCeD AaBboD AaBbcc AaB AaBbce 1 Body Text 1 Heading 1 1 List Par.. 1 No Spac.. 1 Normal 1Table Pa... Heading 2 ite Subtitle Styles 3] (MM/1 queue) You have been asked to analyze a business process that looks as follows: 4 min. 6 min. AND 9 min. Each of the three steps is performed by a dedicated worker (A. B., C) as indicated above Work for a job is doue in parallel along the top and bottom paths. A record kept of incoming jobs seems to indicate that the time between individual job a exponentially distributed with a mean of 12 minutes. Further, assume that the service times are exponentially distributed. What is the length of the critical path in minutes? (Hint Each of the three steps is am MMI queue.) F F2 F3

Explanation / Answer

Critical path is the longest time taking path in a network.

In this path, The critical path is through station (C)

Calcualtions

Average time in system for station A = 1/((Service rate-Arrival rate) = 1/((60/4)-(60/12)) = 0.1 hour

Average time in system for station B = 1/((Service rate-Arrival rate) = 1/((60/6)-(60/12)) = 0.2 hour

Average time in system for station C = 1/((Service rate-Arrival rate) = 1/((60/9)-(60/12)) = 0.6 hour

The path AB is taking 0.1+0.2 = 0.3 hours while path C is taking 0.6 hours. So, it is critical path.

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