In a wireless system for mobile telephony, active terminals making calls in a certain area are assigned one access port. Each of the access ports have in turn been assigned N channels. Calls are...

In a wireless system for mobile telephony, active terminals making calls in a certain area are assigned one access port. Each of the access ports have in turn been assigned N channels. Calls are assumed to have exponentially distributed duration (holding times) and Poisson-distributed arrivals. A call is blocked if all N channels are busy. Show that if N is large, the number of calls in progress in the area in a certain snapshot is approximately Poisson-distributed!