Before completing production, a product must passthrough three stages of production. On the average, a newproduct begins at stage 1 every 6 minutes. The average timeit takes to process the product at each stage is as follows:stage 1, 3 minutes; stage 2, 2 minutes; stage 3, 1 minute.After finishing at stage 3, the product is inspected (assumethis takes no time). Ten percent of the final products arefound to have a defective part and must return to stage 1 andgo through the entire system again. After completing stage3, 20% of the final products are found to be defective. Theymust return to stage 2 and pass through 2 and 3 again. Onthe average, how many jobs are in the system? Assume thatall interarrival times and service times are exponential andthat each stage consists of a single server.

Before completing production, a product must passthrough three stages of production. On the average, a newproduct begins at stage 1 every 6 minutes. The average timeit takes to process the product at each stage is as follows:stage 1, 3 minutes; stage 2, 2 minutes; stage 3, 1 minute.After finishing at stage 3, the product is inspected (assumethis takes no time). Ten percent of the final products arefound to have a defective part and must return to stage 1 andgo through the entire system again. After completing stage3, 20% of the final products are found to be defective. Theymust return to stage 2 and pass through 2 and 3 again. Onthe average, how many jobs are in the system? Assume thatall interarrival times and service times are exponential andthat each stage consists of a single server.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 27P

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