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.

Ships arrive at the port of Houston according to a Poisson process with a mean rate of 2.5 per hour. What is the probability that there will be exactly four arrivals during the given two hour period? 4. a) b) If an arrival occurs at noon, what is the probability that the next arrival will occur before 1:00 pm?

Explanation / Answer

a. Mean rate per hour = 2.5

Mean rate per 2 hours = 5

So, Probability of exactly 4 arrivals in 2 hr period= [(e^(-5))*(5^4)]/ (4!)

                        = (0.0067*625)/24 = 0.175

b. Waiting time <=1

     P(T<=1)= Integration (lower limit=0, upper limit=1) 4e^-et   dt

                        = [-e^(-4t)] for t=0 to t=1

                        = -e^-4 - (-e^-0) = -0.018 – (-1)= 1-0.018= 0.982

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