3. The ticket center at the Hinchliffe Stadium where the NJ Jackals play minor league baseball uses a multiple channel queuing system, as fans arrive, they wait in a single file line for the next available ticket window. On average, it takes 2 minutes to purchase a ticket and fans arrive at the ticket booth at an average rate of 7 customers every five minutes, find the following:
university football
| a. | The minimum number of ticket windows that must be open to allow for a feasible system. |
| b. | When three ticket windows are open, what is the average number of fans waiting in line? |
| c. | When four ticket windows are utilized, what is the probability all windows are empty? |
| d. | When four ticket windows are utilized, what is the average time a fan waits in line? |
| e. | When five ticket windows are utilized, what is the average number of fans waiting in line? |
HINT: Queuing.xlsx calculator tool.
5. SafeBright is a nationalchain for repairing and replacing vehicle windshields. The largest percent of their business is windshield repairs. The Essex County location is currently recruiting a new technician to perform these repairs. Two candidates have applied for the technician position. Sheila Shield just graduated from the training program and expects a $25 per hour wage. Her average service time for a windshield repair is 16 minutes. Wendy Wiper is a veteran technician and is requesting $47 per hour. However, given her extensive experience, on average she is able to do a repair in an average of 13 minutes. To maintain their great reptation, SafeBright estimates that the goodwill cost for customers waiting is $20 per hour (this includes both time spent waiting for service to begin and the time for the repair). Customer’s arrive for windshield repairs at an average of 2.5 per hour.
| a. | What is the average waiting time customers would spend in the system under each applicant? |
| b. | Which applicant should be hired? (Use cost analysis.) |
Analysis of Queuing Systems and Technician Hiring for SafeBright Windshield RepairIntroduction
Queuing systems are fundamental to managing customer flow and service efficiency in various industries. In the context of Hinchliffe Stadium’s ticket center and SafeBright’s windshield repair service, understanding queuing theory can help optimize resources and customer satisfaction. This essay delves into the queuing system at Hinchliffe Stadium and the technician hiring decision at SafeBright.
Queuing System at Hinchliffe Stadium
Hinchliffe Stadium employs a multiple channel queuing system to handle customer ticket purchases for NJ Jackals minor league baseball games. With an average ticket purchase time of 2 minutes and an arrival rate of 7 customers every five minutes, several aspects of the system can be analyzed.
Minimum Number of Ticket Windows
To ensure an efficient system, the minimum number of ticket windows must be determined. This can be calculated using queuing theory formulas, considering the arrival rate, service rate, and desired level of service quality. In this scenario, the number of ticket windows should be sufficient to balance the rate of arrivals and service, preventing excessive waiting times for customers.
Average Number of Fans Waiting (Three Windows)
With three ticket windows open, the average number of fans waiting in line can be calculated. This involves considering the probability distribution of the number of customers in the system and utilizing appropriate queuing theory equations.
Probability of All Windows Being Empty (Four Windows)
When four ticket windows are utilized, the probability that all windows are empty reflects the system’s efficiency. This probability can be computed using queuing theory principles, considering the arrival and service rates.
Average Fan Waiting Time (Four Windows)
The average time a fan waits in line with four ticket windows can be determined through queuing theory calculations. This considers the average time a customer spends in the system, waiting in line and being serviced.
Average Number of Fans Waiting (Five Windows)
Similarly, the average number of fans waiting in line with five ticket windows can be calculated using queuing theory, accounting for the arrival rate and service rate.
Technician Hiring Decision at SafeBright
SafeBright, a national windshield repair chain, faces a hiring decision between two technician applicants: Sheila Shield and Wendy Wiper. The decision involves assessing their service times, wage demands, and customer goodwill cost.
Average Customer Waiting Time
The average waiting time customers spend in the system for each applicant can be evaluated. This entails combining the time customers wait for service initiation and the actual repair time, along with any customer goodwill cost due to waiting.
Cost Analysis for Technician Hiring
To make an informed decision, a cost analysis should be conducted. This involves considering the technician’s wage, repair efficiency, and customer goodwill cost. The total cost for each applicant should include labor cost and potential goodwill cost due to customer waiting.
Conclusion
Queuing theory provides valuable insights into optimizing resource allocation and customer satisfaction in service industries. Analyzing the queuing system at Hinchliffe Stadium and the technician hiring decision at SafeBright exemplifies the practical applications of queuing theory. By calculating metrics such as average waiting times, probability distributions, and costs, businesses can make informed decisions to enhance operational efficiency and customer experience.
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