Question

QUESTIONS For MM: GD queuing system with 2 servers of service rate =40 customers per hour per server and arrival ratei - 45 customers per hour, on the verge, how long in minutes) does a customer wait in line round off to 2 decimal digits) QUESTION 10 A small branch bank has two teller, one for deposits and one fow withdrawals Cistomers arrivent arch teller's window with an average rate of 20 customers per hour. The total customer anivartes per hour) The incrival times are exponenti The service time of ench teller is exponential with a man of 2 minutes The bank manager is considering changing the setup to allow each eller to handle both withdrawals and deposits to avoid the situations that arise from time to time when the queue ble in front of one teller while the other is sile. However since the tellers would b e to handle both deposits and withdrawals, their chciency would decreto sme service time of 2.2 minutes Compare the present system with the proposed system with respect to the total average ber of customers in the banks and the a ncime customer would have to spend in the bank T T 1 T . . . .

Answer 1

Arrival rate = λ = 45 per hour

Service rate = µ = 40 per hour

Traffic intensity = ρ = (λ/ µ) = (45/40) = 1.125

N = 2

Probability P0

$P_{0} = \frac{(1-\rho )}{1-\rho ^{N+1}}$

P0 = (-0.125/(1-1.4238) = 0.0295

Effective Arrival rate = λeff = λ(1-PN) = λ(1-P0ρN)

λeff = 45 x [1 – (0.0295 x 1.125 ^2)] = 43.3198

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