Systems with selective overflow and change of bandwidth

We consider a loss system with n channels and a finite or infinite overflow group, which is offered N different services, all having Poisson arrival processes. All calls have same bandwidth demand and mean service time, but the mean service time may be different on the primary group and the overflow group, corresponding to data traffic with different bandwidth allocation on primary (micro-cell = femto-cell) and overflow group (macro-cell = LTE-cell).

Then using a result of Wallström we can calculate the Binomial moments of the total overflow traffic. Given a certain number of busy channels on the overflow group, we show by balance equations that the number of calls of each service will be Multinomial distributed with probabilities proportional with the arrival rates.

Using a recent result of Newcomer & al, we then find moments (done up to fourth order) of individual overflow streams or any combinations of overflow streams. Thus we can find the correlation between services and for example the moments of some traffic streams which may overflow to one system, whereas other traffic streams may be blocked or overflow to another system.