The 4M company has a work center with a single turret lathe. Jobs arrive at this...

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The 4M company has a work center with a single turret lathe.Jobs arrive at this work center according to a Poisson process at amean rate of 2 jobs per day, The lathe processing time has anexponential distribution with a mean of 0.25 day per job.
a) On average, how many jobs are waiting.in the work center?
b) On average, how long will a job stay in the center?
c).Since each job takes a big space, the waiting jobs arecurrently waiting in the warehouse. The production manager isproposing to add a storage space near the lathe. If an arriving jobwill have at least 90% chance waiting near the lathe, how bigshould be the storage space near the lathe?

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SOLUTION This is a direct application of MM1 Queue System Backup Theory An MM1 queue system is characterized by arrivals following Poisson pattern with average rate this is also the same as exponential arrival with average interarrival time 1 service time following Exponential Distribution with average service time of 1 See Answer

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