Problems: Queuing Problems
Bank of Ohio in Zanesville has a single drive-in teller window. Customers arrive at the window about every 10 minutes on average with an exponential distribution or the hourly arrival rate is λ = 6. It take an average of five minutes (exponentially distributed) to complete each customer order or the hourly service rate is μ = 12. You are asked following tasks:
Determine
- Expected number of customers in the system, including those being served.
- Expected number of customers in the queue, excluding those being served.
- Expected waiting time in the system, including service time, for an individual customer.
- Expected waiting time in the queue, excluding service time, for an individual customer.
- Utilization factor
- The probability that waiting time in the system exceeds 0.25 hours (15 minutes)
- The probability that waiting time in the queue exceeds 0.25 hours (15 minutes)
- The probability that the system has 5 customers in the system
Problem: Computer Simulation
Jack Williams operates a small mechanics shop in his hometown, Lima, Ohio. He works six days a week, Monday thru Friday, 10:00 AM to 6:00 PM and Saturdays from 9:00 AM to 12:00 PM. On a regular weekday, customers' arrival time is exponentially distributed with a mean of 45 minutes and service time is also exponentially distributed with a mean of 35 minutes. Simulate Jack Williams' shop for 100 customer arrivals to estimate Average Time in Line and Average Time in System.