The impact of the traffic characteristics of secondary users (SUs) on the performance of cognitive radio networks (CRNs) should be understood for designing operation rules. This paper focuses on multi-type burst services and network congestion problem in CRNs and evaluates the QoS of SUs based on multiple cross-layer considerations. A two-state Markov-modulate Bernoulli process (MMBP-2) is adopted to model packet flows of SUs with different burst degrees in CRNs. We propose a two-dimensional discrete queuing model to consider spectrum access, burstiness of traffic, network congestion, channel environment, user activity and finite buffer. We construct an iterative algorithm to compute the steady-state distribution of the proposed queuing model and determine the performance metrics like the throughput, the average delay, the average queue length and the total packet loss probability. Numerical analysis evaluates the QoS of SUs under different burst environments.