# Calculate the average number of students in the system

Driving on the highway is analogous to a manufacturing system. Suppose a 4-mile section of highway I70 is our manufacturing system. Cars that drive along route I70 towards the Dayton airport direction represent parts which are being processed in this system. We assume on this particular day, all cars travel towards the same destination, follow the same route, and take the same exit. Discussion Questions 1. According to the video of manufacturing processes, the nature of flow in assembly line is different from that in workcenter (jobshop). The former is regular and sequential, and the latter is jumbled and intermittent. How would you describe the flow of these cars described here? Is this manufacturing system an assembly line or workcenter? And why? 2. If cars on highway I70 have different destinations, come in at different entrances, and take different exits, would your answer to the first question be different? And why? 3. We’ve learned several common process performance measures from Module 4. Let’s apply these concepts to this highway case. What is the concept behind each of the followings? A. The number of cars in the Dayton airport direction on this 4-mile section of highway I70? B. The average number of cars passing at the end of this 4-mile section of highway I70 within an hour? C. The time that takes you to drive through this 4-mile section of highway I70? D. If you know your average speed on this 4-mile section of highway I70 on this particular day, what performance measure would you be able to calculate (inventory, throughput rate, or flow time)? A study-aid desk staffed by a graduate student has been established to answer students’ questions and help in working problems in your OSCM course. The desk is staffed eight hours per day. The dean wants to know how the facility is working. Statistics show that students arrive at a rate of three per hour, and the distribution is approximately Poisson. Assistance time averages 12 minutes, distributed exponentially. Assume population and line length can be infinite and queue discipline is FCFS. a. Calculate the percentage utilization of the graduate student. (Round your answer to 1 decimal place.) b. Calculate the average number of students in the system (excluding the graduate student server).(Round your answer to 3 decimal places.) c. Calculate the average time in the system. (Round your answer to 2 decimal places.) d. Calculate the probability of four or more students being in line or being served. (Round your answer to 4 decimal places.) d. What is the probability that an arriving student (just before entering the Administrative Services Office) will find at least one other student waiting in line? (Round your answer to 4 decimal places.)

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