You are the director of the customer service center in Company Alpha. You find that the mean time between calls to the center is 6 minutes with standard deviation of 4 minutes. The effective response time is 11 minutes with a standard deviation of 20 minutes. (a) Identify the following parameters: t a: ______________ σa: ______________ ca2: ______________ r a: ______________ t e: ______________ σe: ______________ ce2: ______________ r e: ______________ (b) Suppose the customer call center has 4 servers who answer calls. Find the following metrics: u: ______________ c d2: ______________ (c) Assume that 100% of answered calls are then recorded and immediately monitored for the quality purposes. What is the arrival variability at the Quality Office? Why? c a2: ______________ ___________________________________________________________________________ ___________________________________________________________________________
time between calls to the center is 6 minutes with standard deviation of 4 minutes. The effective
response time is 11 minutes with a standard deviation of 20 minutes.
(a) Identify the following parameters:
t a: ______________ σa: ______________ ca2: ______________ r a: ______________
t e: ______________ σe: ______________ ce2: ______________ r e: ______________
(b) Suppose the customer call center has 4 servers who answer calls. Find the following metrics:
u: ______________ c d2: ______________
(c) Assume that 100% of answered calls are then recorded and immediately monitored for the
quality purposes. What is the arrival variability at the Quality Office? Why?
c a2: ______________
___________________________________________________________________________
___________________________________________________________________________
Arrival Rate (λ): This is the rate at which customers arrive at the service center. It's typically measured in customers per unit of time (e.g., calls per minute).
Service Rate (μ): This is the rate at which customers are served by the system or servers. It's also measured in customers per unit of time.
Utilization (ρ): Utilization is a measure of how busy the system or servers are and is calculated as the ratio of the arrival rate (λ) to the product of the service rate (μ) and the number of servers (c). ρ = λ / (μ * c)
Variance (σ^2) and Standard Deviation (σ): Variance measures the spread or variability in a distribution, while the standard deviation is the square root of the variance. In the context of your question, these parameters describe the variability in both the time between customer calls (σ_a) and the effective response time (σ_e).
Coefficient of Variation (CV): This is a relative measure of variability and is calculated as the standard deviation (σ) divided by the mean (t_a or t_e) for the respective parameters. CV = σ / t
Variance of the Number of Customers (c_d2): This is a measure of how the number of customers in the system varies and is calculated based on arrival rate (λ), service rate (μ), and the number of servers (c).
Quality Monitoring: In the context of your question, it's assumed that 100% of answered calls are recorded and monitored for quality purposes. This means that there is no additional variability introduced in the quality monitoring process.
Basic knowledge of probability and statistics: Understanding concepts such as mean, variance, standard deviation, and coefficient of variation will be helpful.
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