Juhn and Sons Wholesale Fruit Distributors employ one worker whose job is to load fruit on outgoing company trucks. Trucks arrive at the loading gate at an average of 26 per day, or 3.25 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 [the utilization rate, time and number in the system and in the queue]. What is the probability that there will be three or more trucks either being loaded or waiting? Discuss the results of your queuing model computation. Juhn believes that adding a second fruit loader will substantially improve the firm’s efficiency. He estimates that a two-person crew, still acting like a single-server system, at the loading gate will double the loading rate from 4 trucks per hour to 8 trucks per hour. Analyze the effect on the queue of such a change and compare the results with those found in (a) above [the utilization rate, time and number in the system and in the queue]. Truck drivers working for Juhn and Sons are paid a salary of $30 per hour on average. Fruit loaders receive about $18 per hour. Truck drivers waiting in the queue or at the loading gate are drawing a salary but are productively idle and unable to generate revenue during that time. What would be the hourly cost savings to the firm associated with employing two loaders instead of one? Juhn and Sons are considering building a second platform or gate to speed the process of loading their fruit trucks. This, they think, will be even more efficient than simply hiring another loader to help out the first platform and will not require any more loaders that it will to put both loaders on one dock. Assume that workers at each platform will be able to load 4 trucks per hour each and that trucks will continue to arrive at the rate of 3.25 per hour.

Find the waiting line’s new operating conditions [the utilization rate, time and number in the system and in the queue].

Is this new approach indeed speedier than the other two already considered?