Customer arrivals at a 7-Eleven is Poisson at the rate of 20 per hour. They can be assumed to spend an average of 12 minutes picking up merchandise, with the length of time having an exponential distribution. Two checkout counters provide service with a service rate of 15 per hour at each counter. We may also assume that the service times have an exponential distribution. Determine the limiting results for the following: (a) the distribution of the number of customers picking up merchandise and its mean.
I understood that entering the store and picking up a merchandise is an M/M/infinity queue model. Since the merchandise picking up time is 12 minutes so the distribution of number of customers picking up the merchandise is POISSON. This means that the mean should be 5, but in M/M/infinity queueing model, mean is r i.e. lambda/mu which here will be 4.
So, what should the mean be by using the Poisson distribution? 4 or 5?