Assuming a 24 hour operation in a warehouse, and an arrival following Poisson distribution with mean rate of 36 per day and service (unloading using a single bay) following exponential distribution with a rate of 48 trucks per day, answer the following question. What is the expected waiting time in the system (in hours) for a typical truck?

The expected value is equal to 0.176

Explanation:

mean = 36

rate per day = 48

P(x; 48)= e⁻⁴⁸( 48)³⁶/36!

E(X)= 1.425 e⁻²¹ 3.347 e⁶⁰/3.72e⁴¹

E(X)= 1.425 *3.347*e⁻²/3.72

E(X)= 1.3e⁻²= 0.1759= 0.176

The probability that an event occurs in a very short time interval is proportional to the length of the interval which is a positive quantity and may be interpreted as the average number of occurrences per unit of time.

The probability that two or more events occur in such a short interval is so small that it can be neglected.

events occurring in non overlapping intervals of time are statistically independent .

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