DAS Brick Distributors currently employs 1 worker whose job is to load bricks on outgoing company trucks. On average, a truck arrives at the loading platform every 20 minutes, according to a Poisson distribution.
The worker loads them at a rate of 4 trucks per hour, following approximately the exponential distribution in his service times. Truck drivers working for DAS earn an average of $10 per hour. Brick loaders receive about $6 per hour. Drivers waiting in the queue or at the loading platform are drawing a salary but are productively idle and unable to generate revenue during that time.
a) Compute the following operating performance measures of the existing system (one loading platform with one worker): - The utilization rate, the average number of trucks in the queue, the average waiting time in the queue, the average number of trucks in the system, the average waiting time in the system, and the probability that the system is empty (that is there are no trucks in the system).
b) The Manager of DAS would like to analyze the system where two workers are employed in one loading platform. He/She estimates that two-person crews at the loading gate will double the loading rate from 4 trucks per hour to 8 trucks per hour. Compute the same operating performance measures as the ones you computed in part (a).
c) Now the manager would like to analyze the third type of system where DAS would build a second platform. There will be only one worker at each platform, loading bricks at a rate of 4 trucks per hour, and trucks will continue to arrive at a rate of 3 trucks per hour. Compute the new operating characteristics (same as part (a) and part (b)).
d) Compare the three systems and make a recommendation to DAS Brick Distributors as to whether they should keep the existing system or change to one of the two systems you helped them analyze.