The focus of this paper is the IEEE 802.11e MAC layer modeling under slow time varying Rayleigh fading channel via both layered and multi-layered design approaches and through non Markovian Stochastic Petri Nets (NMSPN). In this paper, we carry out extensions to SPN IEEE 802.11 compact model reported in. Towards that, we investigate relaxation accounting for slow Rayleigh fading, service differentiation and cross-layer design. We propose two MAC IEEE 802.11e models including many of the EDCF extensions and accounting for slow Rayleigh fading. The first one is non cross-layer based whereas the second is cross-layer based. The cross-layer design approach adopted enables to not only manage collisions but also mitigate fading effects. We show the expected throughput behavior with respect to the virtual load at MAC level and the impact of service differentiation on MAC performance. For further information, please visit this web site.