Which property of the queuing diagram indicates that when no queue is present, the departure rate equals the arrival rate?

The correct understanding revolves around the property of the system when it is operating under steady state conditions. In queuing theory, when there is no queue — meaning no waiting time for customers — the system operates at its full capacity. Therefore, in this scenario, the departure rate matches the arrival rate.

This relationship between the departure and arrival rates occurs because if customers arrive at the service facility but are not being serviced immediately (resulting in a queue), the departure rate would be less than the arrival rate. However, when the system is balanced and operating efficiently—without any backlog—every customer that arrives can be serviced immediately. Hence, the departure rate will equal the arrival rate.

Understanding this concept is crucial for analyzing the performance of queuing systems in various applications, particularly in civil engineering contexts where systems, like traffic management and service facilities, are involved. The other options do not directly address the core relationship between arrival and departure in the absence of a queue, making them less relevant in this context.