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use the single-server drive-up bank teller operation referred to in problems 1 and 2 to determine the following operating characteristics for the system: a. the probability that no customers are in the system b. the average number of customers waiting c. the average number of customers in the system

Sagot :

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(a) The probability that there are no clients in the system is 0.3333

(b) The average number of customers waiting is 1.33

(c) The average number of customers in the system is 2

(d) The average time a customer spends waiting is 3.33 min

(e) The average time a customer spends in the system is 5 min

(f) The probability that arriving customers will have to wait for service is 0.6667.

Given that,

Customers of Willow Brook National Bank can conduct financial transactions at a drive-up teller window without getting out of their cars. On weekday mornings, the drive-up teller window receives 24 customers each hour, or 0.4 customers per minute, arriving at random.

Arrival rate λ = 24 customers per hour or 0.4 customers per minute

Service rate  μ​ = 36 customers per hour or 0.6 customers per minute

Utilizing the single-server drive-up bank teller operation previously mentioned, establish the following system operational characteristics:

(a) The probability that there are no clients in the system is

P₀ = 1 - λ /μ

= 1 - (24/36)

= 1/3

= 0.3333

(b) The average number of customers waiting

Lq = λ²/ [μ(μ - λ)]

= 242/[36×(36-24)]

= 1.33

(c) the average clientele using the system.

L = Lq + λ/μ  

= 1.33 + (24/36)

= 2

(d)the average length of time a consumer must wait.

Wq = λ/ [μ(μ - λ)]

= 24/[36×(36-24)]

= 0.0555 hr

= 3.33 min

(e) The average time a customer spends in the system

W = Wq + 1/μΧ

= 0.0555 + (1/36)

= 0.0833 hr

= 5 min

(f) the probability that clients who arrive will have to wait for service.

= 1 - P₀

= 1 - 0.3333

= 0.6667

To learn more about probability visit: https://brainly.com/question/11234923

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