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

Answer:

Lq = 1.680

time taken by customer 20.03 min

Step-by-step explanation:

Given data:

m = 6

a = 3 min

p = 15 minutes

$u = \frac{p}{am}$

$u = \frac{15}{3\times 6} = \frac{15}{18} = 0.833$

CVa = 1

$CVp =\frac{5}{15} = 1/3$

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

$Lq = 0.833^{\sqrt{\frac{2\times (6+1)\times (1^2+(1/3)^2}{2\times (1-0.833}}$

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