### Question 33

Two branches, each of which has one automatic teller machine, are to be integrated. One automatic teller machine is to be installed at the integrated branch. Which of the following formulas determines the average waiting time for the automatic teller machine after integration? In this example, the waiting time is based on the M/M/1 queuing model, and the average waiting time does not include the service time.

[Conditions]

(1) Average service time: T_{s}

(2) System utilization before integration: ρ for both branches

(3) The number of users after the integration is the total number of users of the two branches before the integration.

a | 1 | ×Ts | b | ρ | ×Ts | c | 1 | ×Ts | d | 2ρ | ×Ts | ||||

1－ρ | 1－ρ | 1－2ρ | 1－2ρ |

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