Problem 1 (25 pts):

At a hub airport, passengers arrive one at a time through the entrance with interarrival times distributed exponential with mean 0.5 minute (all times are in minutes unless other- wise noted). Of these passengers 35% goto the manual check-in counter, 50% go right to the kiosks, and the remaining 15% don’t need to check in at all and proceed directly to the security (it takes these latter types of passengers between 3 and 5 minutes, uniformly  distributed, to walk from the entrance to the security area. There are two-agents at the manual check-in station, fed by a single FIFO queue. Manual check-in times follow atri- angular distribution between 1 and 5 minutes with a mode of 2 minutes.  After manual check-in, passengers walk to the security area, which takes them about 2.0 and 5.8 minutes, uniformly distributed.  There are two kiosks (two stations) fed by a single FIFO queue. Check-in times for using kiosks are triangularly distributed between 0.5 and 1.5 minutes with a mode of 1. After check-in, passengers walk to the security area, taking be- tween 1 and 3 minutes, uniformly distributed. All passengers eventually get to the secu-rity area, where there are six stations fed by a single FIFO queue. Security-check times are triangularly distributed between 1 and 6 minutes with a mode of 2.

Simulate this system for one replication of an 8-hour period and show:

1)  the average queue length, average times in queue, and average time in system of pas- sengers for EACH passenger type.

2) the average queue length, average times in queue, and average time in system of pas- sengers for all passenger types COMBINED.

Problem 2 (25 pts):

A state driver’s license exam center would like to examine its operation for potential im- provement. Arriving customers enter the building and take a number to determine their place in line for the written exam, which is self administered by one of five electronic testers. The testing times are distributed as EXPO(8); all times are in minutes. Thirteen percent of the customers fail the test. These customers are given a booklet on the state  driving rules for further study and leave the system.

The customers who pass the test select one of two photo booths where their picture is taken and the new license is issued. The photo booth times are distributed TRIA(2.6, 3.6, 4.3). The photo booths have separate lines, and the customers enter the line with the few- est number of customers waiting in queue. If there is atie in queue length, they enter Booth 1. If there is no queue, they also enter Booth 1, whether it is busy or not. Note that customers cannot see into the photo booths.

The center is open for arriving customers eight hours a day, although the services are continued for an additional hour to accommodate the remaining customers.  The cus- tomer arrival pattern varies over the day and is summarized below:

Hour         Arrivals per Hour

1                      17

2                      28

3                      40

4                      31

5                       35

6                      43

7                      29

8                       22

Run your simulation for ten days, keeping statistics on 1) the average number of test fail- ures per day; 2) utilization for electronic-tester, photo-booth1, and photo-booth2 utiliza-tion, respectively; 3) average number in electronic-tester queue, in photo-booth1 queue,   and in photo-booth2, respectively; and 4) average customer system time for those cus-tomers passing the written exam.

Problem 3 (25 pts):

Apart arrives every 10 minutes to a system having three workstations (A, B, and C), where each workstation has a single machine; the first part arrives at time 0. There are four part types, each with equal probability of arriving. The process plans for the four part types are given here. The entries for the process times are the parameters for a triangular distribution (in minutes).

Assume that the transfer time between arrival and the first station, between all stations, and between the last station and the system exit is 3 minutes. Use the Sequence feature to direct the parts through the system and to assign the processing times at each station. Use the Sets feature to collect cycle times (total times in system) for each of the part types separately. Run the simulation for a single replication of length 10,000 minutes, and collect statistics on the average part cycle time.