The key assumption for the single server queue model is that the average interarrival time is greater than the average process time.
This assumption means that, on average, customers arrive at the queue less frequently than they are served. In practical terms, it implies that the server can handle incoming traffic adequately without becoming overwhelmed. If the average interarrival time were less than the average service time, the queue would become longer over time as more customers arrive than the server can process, leading to longer wait times and potential system overload.
So, maintaining an average interarrival time greater than the average service time is crucial for ensuring smooth operation and efficiency within a single server queue system.