(Solved): 1. Consider the following production line consisting of 4 machines: M2 Cinta transportadora Cinta t ...

1. Consider the following production line consisting of 4 machines: M2 Cinta transportadora Cinta transportadora 0 M 02 M M4 The products are transported to the M1 machine through a conveyor belt according to a Poisson Process with an average time between arrivals of 1 minute and 12 seconds. When machine M1 is busy and a new product arrives it must wait in queue Q1 according to a FIFO discipline. M1 can process an average of 60 jobs per hour, with exponentially distributed individual processing time. After finishing their treatment in M1, the products are sent to finish their process to one of the M2, M3 or M4 machines. If these three machines are busy then the product must wait in queue Q2 (also with FIFO discipline). Service times on M2, M3 and M4 machines are exponentially distributed with an average of 3 minutes. Calculate: The average number of jobs in Q1 and Q2, the expected time a product spends on this production line (time spent on conveyor belts is ignored), and the proportion of time that the production line is idle.