This paper presents a new approach to provide stochastic delay guarantees via fully distributed model-based call admission control for IEEE 802.11 single-hop ad hoc networks. We propose a novel stochastic link-layer channel model to characterize the variations of the channel service process in a non-saturated case using a Markov-modulated Poisson process (MMPP) model. We use the model to calculate the effective capacity of the IEEE 802.11 channel. The channel effective capacity concept is the dual of the effective bandwidth theory. Our approach offers a tool for distributed statistical resource allocation in ad hoc networks, which combines both efficient resource utilization and quality-of-service (QoS) provisioning to a certain probabilistic limit. Simulation results demonstrate that the MMPP link-layer model and the calculated effective capacity can be used effectively in allocating resources with stochastic delay guarantees.