Stability of a Markov-modulated Markov Chain, with Application to a Wireless Network Governed by two Protocols

References

• Abramson, N. (1970). The ALOHA System — Another Alternative for Computer Communications. AFIPS Conference Proceedings. 36, 295–298.Google Scholar
• Andreev, S., Dubkov, K., Turlikov, A. (2010). IEEE 802.11 and 802.16 cooperation within multi-radio stations. Wireless Personal Communications, Springer Science+Business Media B.V., 1–19.Google Scholar
• Berlemann, L., Hoymann, C., Hiertz, G.R., Mangold, S. (2006). Coexistence and interworking of IEEE 802.16 and IEEE 802.11(e). IEEE 63rd Vehicular Technology Conference, 1, 27–31.Google Scholar
• Bonald, T., Borst, S., Hedge, N., Proutiere, A. (2004). Wireless Data Performance in Multi-Cell Scenarios. Proc. of ACM SIGMETRICS, 378–387.Google Scholar
• Bordenave, C., McDonald, D., Proutiere, A. (2008). Performance of Random Muedium Access Control, An Asymptotic Approach. Proc. of ACM SIGMETRICS/Performance, 1–12.Google Scholar
• Borovkov, A.A. (1998). Ergodicity and Stability of Stochastic Processes, Wiley. MR1658404Google Scholar
• Borst, S., Jonckheere, M., Leskelä, L. Stability of parallel queueing systems with coupled service rates. Discrete Event Dynamic Systems, 18, 4, 447–472. MR2443653Google Scholar
• Bramson, M. (2008). Stability of queueing networks, Probab. Surveys, 5, 169–345. MR2434930Google Scholar
• Dai, J.G. (1995). On positive Harris recurrence of multiclass queueing networks: A unified approach via fluid limits. Annals Applied Probability, 5, 49–77. MR1325041Google Scholar
• Dai, J.G. and Meyn, S.P. (1995). Stability and convergence of moments for multiclass queueing networks via fluid limit models. IEEE Transactions on Automatic Control., 40, 11, 1889–1904. MR1358006Google Scholar
• Ephremides A., Hajek, B. (1998). Information Theory and Communication Networks: an Unconsummated Union. IEEE Transactions on Information Theory. 44, 2416–2434. MR1658779Google Scholar
• Foss, S., Konstantopoulos, T. (2004). An overview of some stochastic stability methods. Journal of Operation Research Society Japan, 47, 275–303. MR2174067Google Scholar
• Gamarnik, D. (2004). Stochastic bandwidth packing process: stability conditions via Lyapunov function technique. Queueing systems, 48, 339–363. MR2104109Google Scholar
• Gamarnik, D., Squillante, M. (2005). Analysis of stochastic online bin packing processes. Stochastic Models, 21, 401–425. MR2148766Google Scholar
• Kifer, Yu. (1986). Ergodic theory of random transformations. Progress in Probability and Statistics, Birkhauser. MR0884892Google Scholar
• Lindvall, T. (2002). Lectures on the Coupling Method, 2nd edition, Dover. MR1924231Google Scholar
• Litvak, N., Robert, P. (2012). A scaling analysis of a cat and mouse Markov chain. Annals of Probability, 22, 2, 792–826. MR2953569Google Scholar
• Meyn, S.P. (2007). Control Techniques for Complex Networks, Cambridge University Press. MR2372453Google Scholar
• Meyn, S.P., Tweedie, R.L. (1993). Markov Chains and Stochastic Stability, Springer Verlag. MR1287609Google Scholar
• Mikhailov, V.A., Tsybakov, B.S. (1979). Ergodicity of a Slotted ALOHA System. Problems of Information Transmission, 15, 301–312. MR0581656Google Scholar
• Roberts, L. (1972). ALOHA Packet System with and without Slots and Capture. Advanced research projects agency, Network information center, Tech. Rep. ASS Note 8.Google Scholar
• Shah, D., Shin, J. (2012). Randomized scheduling algorithm for queueing networks. Annals of Applied Probability, to appear. MR2932544Google Scholar
• Thorisson, H. (2000). Coupling, Stationarity, and Regeneration, Springer Verlag. MR1741181Google Scholar
• Walke, B., Mangold, S., Berlemann, L. (2007). IEEE 802 wireless systems: Protocols, multi-Hop mesh/relaying, performance and spectrum coexistence. NJ: Wiley.Google Scholar
• Zhu, J., Waltho, A., Yang, X., Guo, X. (2007). Multi-radio coexistence: Challenges and opportunities. Proceedings of 16th International Conference on Computer Communications and Networks, 13–16, 358–364.Google Scholar