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Juhn and Sons Wholesale Fruit Distributors employ one worker whose Job 1S to loa

ID: 438452 • Letter: J

Question

Juhn and Sons Wholesale Fruit Distributors employ one worker whose Job 1S to load fruit on outgoing company trucks. Trucks arrive at the loading gate at an average of 24 per day, or 3 per hour, according to a Poisson distribution. The worker loads them at a rate of 4 per hour, following approximately the exponential distribution in service times. Determine the operating characteristics of this loading gate problem. What is the probability that there will be more than three trucks either being loaded or waiting? Discuss the results of your queuing model computation.

Explanation / Answer

queuing model computation as follows

is the mean arrival rate and = 3

is the mean service rate = 4

operating characteristics of this loading gate problem = = / = 3/4 = 0.75

So probability that there will be more than three trucks either being loaded or waiting = 3 trucks are in the system

L = 3

P3 = 3 * P0 = 3 * (1- ) = (0.75)3 * 0.25

= 0.1054