Question

. You are working at a bank and doing resource planning. You think that there should be six tellers working in the bank. Tellers take 15 minutes per customer with a standard deviation of 5 minutes. On average one customer arrives every three minutes according to an exponential distribution. a. On average how many customers are waiting in line? b. On average how long would a customer spend in the bank?

Answer 1

Lq = 1.680

time taken by customer 20.03 min

Explanation:

Given data:

m = 6

a = 3 min

p = 15 minutes

`u = (p)/(am)`

`u = (15)/(3* 6) = (15)/(18) = 0.833`

CVa = 1

`CVp =(5)/(15) = 1/3`

Number of customer waiting in line =
`Lq = utilization ^{\sqrt{(2 * (number \ of servers + 1 ) * (CVa^2 + CVs^2))/(2* (1- utilization))}`

`Lq = 0.833^{\sqrt{(2* (6+1)* (1^2+(1/3)^2)/(2* (1-0.833)}`

Lq = 1.679158

Lq = 1.680

FROM QUENNING FORMULA WE GET Tq = 5.039

so, time taken by customer = 5.039 + 15 = 20.03 min