The IETF developed two main approaches to provide QoS aware services in the Internet: Integrated Services (IntServ) and Differentiated Services (DiffServ). Both have well known pros and cons (e.g., [Huston, 24; Bernet et al., 2]). The stateful IntServ has a greater level of accuracy and a finer level of granularity. The stateless DiffServ possesses excellent scaling properties, but lacks a standardized admission control scheme and, upon overload in a given service class, degradation of service can occur. To provide QoS in DiffServ, three possible strategies are: (i) plain and heavy over-dimensioning; (ii) admission control at the borders of the DiffServ region, coupled with suitable assumptions on the distribution of the traffic within the region, which can lead to over-dimensioning, even if less severe than the previous one; (iii) per-node admission control within the region. Following RFC2990, we recently proposed an “admission control function which can determine whether to admit a service differentiated flow along the nominated network path” [Huston, 24], i.e., the third of the above strategies. This function, named GRIP (Gauge and Gate Reservation with Independent Probing), can provide strict QoS guarantees by means of stateless DiffServ-compliant procedures. This feature is paid with a potential loss of efficiency, with respect to an ideal, stateful admission control. The goal of this paper is to evaluate analytically such loss of efficiency, in a specific heterogeneous scenario. In other words, we want to estimate how much resources we can waste if we go stateless and avoid state maintenance functions. The comparison between stateless and stateful approaches is performed under the constraint of strictly offering the same performance levels, in terms of, e.g., loss probability and delay.