In this paper we consider a generalization of M/GI/N/ queues, in which customer capacity is an additional parameter of the system and it is independent of the service time. In more detail we focus on the distributions of the total capacity of customers in the different elements of the queue (waiting line, service and entire system) and provide approximate expressions for the corresponding characteristic functions. To verify the goodness of the proposed approximation, several sets of simulations have been carried out, considering discrete and continuous distributions of the customer capacity and using the Kolmogorov distance as a measure of similarity.