In this paper we develop approximate models for trunk reservation in multi-service systems with BPP (Binomial-Poisson-Pascal) multi-rate traffic streams. The approximation is a generalization of previous work by Tran-Gia & Hübner who assumed Poisson arrival processes. It is based on a generalized algorithm which allows for calculation of individual performance measures for each service, in particular the traffic congestion. The algorithm is numerically robust and requires a minimum of computer memory and computing time. The approximation is good when the services have equal mean service times.