This is under Operations Management or Operations Research of Industrial Enginee

Question

This is under Operations Management or Operations Research of Industrial Engineering. Topic is called Queueing Theory. Manufacturing Systems Modeling and Analysis Second Edition. Please do process.

4.4. Consider a job with processing time distribution parameters E[T] - 3 hours and C2T] 2. The machine breakdown and repair time characteristic parameters are: EF] EIR] 1 hr and CR] 1 7 hr and C2[F]-1, (C[F] is required to be 1) Find the parameters of the effective processing time: E [Tej, vlzj, and C27

Explanation / Answer

Given,

E[T]=3 Hrs

C2[T]=2

E[F]=7 Hrs

C2[F]=1

E[R]=1 Hrs

C2[R]=1

Step 1: Calculate processor availability a:

                        a= E[F] / (E[F]+ E[R]) = 7/(7+1)=7/8 = 0.875

Step 2: Calculate E[Te]:

            E[Te]= E[T]/a = 3/0.875 = 3.428 hrs

Step 3: Calculate C2[Te]:

            C2[Te]= C2[T] + (((1+C2[R])a(1-a)E[R])/E[T])

                        = 2 + (((1+1)*0.875* 0.125 * 1)/3)

                        = 2.0729

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