Virtual Private Network (VPN) dedicated to a customer using a physical transmission network based upon Multi-Protocol Label Switching (MPLS) technology including a plurality of Provider (P) devices and a plurality of Provider Edge (PE) devices, the customer owning at least two specific Customer Edge (CE) devices amongst a plurality of CE devices, a specific CE device being attached to a specific PE device and enabling the customer to gain access to any other CE device belonging to the same VPN, by the intermediary of PE devices to which are attached the CE devices. The VPN comprises several billing zones (10, 12, 14) being each defined by the application of a single flat rate. A PE device (18) belonging to each billing zone includes a virtual router (58, 60, 62) associated with each billing zone, two virtual routers being interconnected by a virtual circuit (38, 40, 42) transmitting all the traffic exchanged between the two associated billing zones so that the traffic flowing between the two billing zones can be measured and therefore precisely billed to the customer.