I was reading about the
M/M/1 Queue and that we assume new customers arrive according to a Poisson distribution, and each customer takes an amount of time to service that is drawn from an exponential distribution?
I understand what it means to have an arrival rate based on Poisson distribution - if an average of 10 come per hour, you'll have 9 a few times, 6 very infrequently, 11 pretty often etc - but what does it mean that service is exponential?
Does this mean that as you serve more customers, the average time it takes to service them rises exponentially? Wouldn't the system crash soon after a few customers?