Question

In a D/D/1 queueing systems, the arrival rate and service rate are equal to 9 customers/hour and 12 customers/hour, respectively. What is the average queue length?

Answer 1

In a D/D/1 queueing system, the average queue length is equal to the average arrival rate multiplied by the average time spent in the system. In this case, the average queue length is 3/4 customer.

Step-by-step explanation:

In a D/D/1 queueing system, the average queue length can be calculated using Little's Law, which states that the average queue length is equal to the average arrival rate multiplied by the average time spent in the system. In this case, the arrival rate is 9 customers/hour and the service rate is 12 customers/hour.

Let's calculate the average queue length:

1. First, we need to calculate the average time spent in the system. Since the service rate is equal to 12 customers/hour, the average service time is 1/12 hour per customer.
2. Next, we can calculate the average queue length using Little's Law: Average Queue Length = Average Arrival Rate * Average Time Spent in the System. Average Queue Length = 9 customers/hour * 1/12 hour/customer = 3/4 customer.