Consider a bank with one teller, an average arrival rate of six customers per hour, and an average service rate of eight customers per hour. Assume that the coefficient of variation of both the service time distribution and the arrival time distribution is 1.0. Calculate the average number of customers in the service (Ns). Select one: a. 2.25 b. 1.00 c. 0.75 d. 3

Consider a bank branch that has three distinct customer arrival patterns throughout the day, as measured by average arrival rates (below). Morning (8:30 - 11:30): arrival 1 = 47 per hour. %3D Lunch (11:30 - 1:30): arrival 2 = 70 per hour. Afternoon (1:30 - 4:00): arrival 3 = 30 per hour. Regardless of the time of day, the average time it takes for a teller to serve customers is 3.17 minutes. Because of competition with other banks in the area, management has developed an internal goal to keep the average customer wait before service to be less than 4 minutes. With that in mind, answer the following: a. During the morning period, what is the minimum number of tellers that the bank needs to hire to achieve the 4-minute service goal mentioned above? [ Select] b. During lunch, what is the minimum number of tellers that the bank needs to hire to achieve the 4 minute service goal mentioned above? [ Select ] c. In the afternoon, what is the minimum number of tellers that the bank

Consider a Poisson queue with random arrivals at the rate of 12 customers per hour and the following steady- state probabilities: po = 1/3, p1 = 1/2, p2 = 1/6, and p, = 0 for n = 3,4,5, ... . What is the mean (or effective) arrival rate in customers per hour for this queuing system? Consider drawing a rate diagram to assist in your solution. O 10 12 O none of the other choices O 2

The office has a single line for customers waiting for the next available clerk. There are two clerks who work at the same rate. On average customers arrive every 8 minutes and the average service rate is 5 per hour for each of the two clerks. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. b.) What proportion of time are both clerks idle? c.) Counting each person being served and the people in line, on average, how many customers would be in this system?

Please do not give solution in image format thanku 1. A single server queuing system with a Poisson arrival rate and exponential service time has an average arrival rate of 13 customers per hour and an average service rate of 20 customers per hour. The average length of time customers will spend in the system is: Select one: a. 0.09286 minutes b. 0.1429 minutes c. 8.571 minutes d. 5.571 minutes 2. A single server queuing system with a Poisson arrival rate and exponential service time has an average arrival rate of 10 customers per hour and an average service rate of 13 customers per hour. The probability of 3 customers in the system is : Select one: a.0.895 b.0.5448 c.0.2308 d.0.105

Describe the important operating characteristics of a queuing system. Be sure to provide examples to illustrate your understanding of these concepts.