Final answer:
A server might be idle with customers waiting in a pooled queuing system because the servers are grouped and serve a common line, allowing for idle moments during customer assignment. Option C is correct.
Step-by-step explanation:
In a queuing system, it is possible for a server to be idle while a customer is waiting, primarily in a situation known as pooled queuing. In a pooled queuing system, servers are grouped together, and the customers are in one line for all servers. This system allows for one server to be momentarily idle while the customer in the front of the queue is being assigned, even when there is a line behind them.
However, this scenario is highly improbable in a single server queue since there is only one line and one server; if the server is idle, there are no customers waiting. A multiple server setup could see a server idle due to the uneven distribution of customers across different lines, but this would likely mean there is no waiting customer for that specific server. Lastly, in a separate queuing system, each server has its own line, and customers would directly go to an available server, making it less likely for a server to be idle while customers are waiting.