Time-critical applications for wireless sensor networks (WSNs) are an important class of services supported by the standard IEEE 802.15.4. Control, actuation, and monitoring are all examples of applications where information must be delivered within some deadline. Understanding the delay in the packet delivery is fundamental to assess performance limitation for the standard. In this paper we analyze the guaranteed time slot (GTS) allocation mechanism used in IEEE 802.15.4 networks for time-critical applications. Specifically, we propose a Markov chain to model the stability, delay, and throughput of GTS allocation. We analyze the impact of the protocol parameters on these performance indexes. Monte Carlo simulations show that the theoretical analysis is quite accurate. Thus, our analysis can be used to design efficient GTS allocation for IEEE 802.15.4.