We investigate a commonly used power control scheme called single-step power control (SSPC) in finite state Markov channel (FSMC). The performance of SSPC is highly affected by two major factors, the power control error (PCE) and the imperfect feedback of the SSPC commands. In the first part of this work, we aim at modelling the behavior of PCE in FSMC. Based on the proposed PCE model, BER and PER performance are evaluated. Simulation results have shown the validity of the proposed PCE model, derived PER and BER in this work. In the second part of this work, SSPC models under different scenarios are established in order to understand the impact of the imperfect feedback on SSPC commands and to obtain the interactions between SSPC and FSMC. We consider four scenarios, perfect feedback, command error, command loss and command delay. The associated transitional probabilities of each scenario are given. Extensive simulation has shown the accuracy of the proposed SSPC models in these four scenarios.

Peer-to-Peer (P2P) networks have been proposed as one promising approach to provide better scalability for Networked Virtual Environment (NVE) systems, but P2P-NVE also increases the probability of cheating by allowing users to manage the states of objects. In this paper, we propose Delaunay State Management (DSM), a P2P-NVE state management scheme that divides the whole virtual world into many triangular regions by Delaunay triangulation. In DSM, each region is managed by three super-peers, whose collective decisions determine how states will change. Assuming that at most one of the three super-peers is malicious, effective anti-cheating can be provided. Additionally, we also describe how DSM provides the essential features for a state management system, such as consistency, load-balancing, and fault-tolerance. Finally, we discuss some of DSM's potential applications.