When a queueing system is modeled as an M/M/1 queue, it is assumed that the arrival time of jobs has Poisson distribution and the service rate has exponential distribution. I am wondering what features a system should have in order to model the arrival rate as Poisson? I known that Poisson is the only distribution that its inter-arrival time of jobs is exponentially distributed which is memoryless. Are there any better and more intuitive features for it?
Also even in a more complex modeling (M/G/1), only the service rate is changed to general which means that the Poisson arrival rate is good enough where G/M/1 or G/G/1 is not as appealing as the previous ones.