In this paper, a novel queueing analytical framework is proposed to evaluate the performance of IEEE 802.15.6-based carrier-sense multiple access with collision avoidance (CSMA/CA) scheduling in wireless body area networks with joint consideration of instantaneous delay constraints and body shadowing effects. Specifically, we develop an absorbing Markov chain to model the medium access process with error controls that is defined by the IEEE standard and design a random time-limited single vacation to describe the potential body shadowing interruption process. To guarantee the timeliness of received packets and avoid energy waste for transmitting valueless packets, an instantaneous delay constraint is carefully considered, which is then characterized by an overdeadline packet dropping process with a predefined waiting deadline. In our analysis, a Markovian arrival process is also adopted to capture the correlation of arrival traffic, and all other random processes are modeled by phase-type distributions, which make our framework more general and comprehensive. To address the inherent complexity of the original model, based on the transient queueing analysis, we develop a buffer-overflowing queueing principle to approximate the overdeadline packet dropping principle by solving a buffer length optimization problem. After that, we construct a multidimensional discrete-time Markov chain to analyze the stationary distribution through the matrix-geometric method. Performance measures, including the average delay, waiting time distribution, and packet transmission failure probability, are derived. The accuracy of our proposed analytical framework is validated by extensive simulations.