# American Institute of Mathematical Sciences

July  2011, 7(3): 677-697. doi: 10.3934/jimo.2011.7.677

## Analysis of globally gated Markovian limited cyclic polling model and its application to uplink traffic in the IEEE 802.16 network

 1 Department of Telecommunications, Budapest University of Technology and Economics, Budapest

Received  September 2010 Revised  May 2011 Published  June 2011

In this paper we introduce the globally gated Markovian limited service discipline in the cyclic polling model. Under this policy at most K customers are served during the server visit to a station among the customers that are present at the start of the actual polling cycle. Here the random limit K is the actual value of a finite state Markov chain assigned to the actual station. The model enables asymmetric Poisson arrival flows and each station has an individual Markov chain. This model is analyzed and the numerical solution for the mean of the stationary waiting time is provided.
This model is motivated by the problem of dynamic capacity allocation in Media Access Control of wireless communication networks with Time-Division Multiple Access mechanism. The "globally gated" character of the model is the consequence of the applied reservation mechanisms. In a fixed length frame after allocating the required capacity for the delay sensitive real-time traffic the random remaining capacity is shared among the subscriber stations for the non real-time traffic. The Markovian character of the random limits enables to model the inter frame dependencies of the required real-time capacity at each station individually.
In the second part of the paper the application of this model to the uplink traffic in the IEEE 802.16 network is discussed.
Citation: Zsolt Saffer, Miklós Telek. Analysis of globally gated Markovian limited cyclic polling model and its application to uplink traffic in the IEEE 802.16 network. Journal of Industrial & Management Optimization, 2011, 7 (3) : 677-697. doi: 10.3934/jimo.2011.7.677
##### References:
 [1] S. Andreev, Zs. Saffer and A. Anisimov, "Overall Delay Analysis of IEEE 802.16 Network,", Int. Workshop on Multiple Access Comm. (MACOM), (2009).   Google Scholar [2] O. J. Boxma, H. Levy and U. Yechiali, Cyclic reservation schemes for efficient operation of multiple-queue single-server systems,, Annals of Operations Research, 35 (1992), 187.  doi: 10.1007/BF02188704.  Google Scholar [3] Y.-J. Chang, F.-T. Chien and C.-C. J. Kuo, Delay analysis and comparison of OFDM-TDMA and OFDMA under IEEE 802.16 QoS framework,, IEEE Global Telecomm. Conf. (GLOBECOM), 1 (2006), 1.   Google Scholar [4] S. Forconi, G. Iazeolla, P. Kritzinger and P. Pillegi, "Modelling Internet Workloads for IEEE 802.16,", Technical Report CS08-03-00, (2008), 08.   Google Scholar [5] R. Iyengar, P. Iyer and B. Sikdar, Delay analysis of 802.16 based last mile wireless networks,, IEEE Global Telecommunications Conference (GLOBECOM), 5 (2005), 3123.  doi: 10.1109/GLOCOM.2005.1578332.  Google Scholar [6] Zs. Saffer, An introduction to classical cyclic polling model,, Proc. of the 14th Int. Conf. on Analytical and Stochastic Modelling Techniques and Applications (ASMTA'07), (2007), 59.   Google Scholar [7] Zs. Saffer and M. Telek, Stability of periodic polling system with BMAP arrivals,, European Journal of Operational Research, 197 (2009), 188.  doi: 10.1016/j.ejor.2008.05.016.  Google Scholar [8] Zs. Saffer and M. Telek, Unified analysis of $BMAP$/$G$/$1$ cyclic polling models,, Queueing Systems, 64 (2010), 69.  doi: 10.1007/s11134-009-9136-7.  Google Scholar [9] C. So-In, R. Jain and A.-K. Tamimi, Capacity evaluation for IEEE 802.16e mobile WiMAX,, Journal of Computer Systems, 2010 (2010), 1.  doi: 10.1155/2010/279807.  Google Scholar [10] Standard IEEE 802.16-2009, Part 16: Air Interface for Broadband Wireless Access Systems, Standard for Local and Metropolitan Area Networks,, May 2009., (2009).   Google Scholar [11] H. Takagi, "Analysis of Polling Systems,", MIT Press, (1986).   Google Scholar [12] A. Vinel, Y. Zhang, Q. Ni and A. Lyakhov, Efficient request mechanism usage in IEEE 802.16,, IEEE Global Telecommunications Conference (GLOBECOM), 1 (2006), 1.   Google Scholar

show all references

##### References:
 [1] S. Andreev, Zs. Saffer and A. Anisimov, "Overall Delay Analysis of IEEE 802.16 Network,", Int. Workshop on Multiple Access Comm. (MACOM), (2009).   Google Scholar [2] O. J. Boxma, H. Levy and U. Yechiali, Cyclic reservation schemes for efficient operation of multiple-queue single-server systems,, Annals of Operations Research, 35 (1992), 187.  doi: 10.1007/BF02188704.  Google Scholar [3] Y.-J. Chang, F.-T. Chien and C.-C. J. Kuo, Delay analysis and comparison of OFDM-TDMA and OFDMA under IEEE 802.16 QoS framework,, IEEE Global Telecomm. Conf. (GLOBECOM), 1 (2006), 1.   Google Scholar [4] S. Forconi, G. Iazeolla, P. Kritzinger and P. Pillegi, "Modelling Internet Workloads for IEEE 802.16,", Technical Report CS08-03-00, (2008), 08.   Google Scholar [5] R. Iyengar, P. Iyer and B. Sikdar, Delay analysis of 802.16 based last mile wireless networks,, IEEE Global Telecommunications Conference (GLOBECOM), 5 (2005), 3123.  doi: 10.1109/GLOCOM.2005.1578332.  Google Scholar [6] Zs. Saffer, An introduction to classical cyclic polling model,, Proc. of the 14th Int. Conf. on Analytical and Stochastic Modelling Techniques and Applications (ASMTA'07), (2007), 59.   Google Scholar [7] Zs. Saffer and M. Telek, Stability of periodic polling system with BMAP arrivals,, European Journal of Operational Research, 197 (2009), 188.  doi: 10.1016/j.ejor.2008.05.016.  Google Scholar [8] Zs. Saffer and M. Telek, Unified analysis of $BMAP$/$G$/$1$ cyclic polling models,, Queueing Systems, 64 (2010), 69.  doi: 10.1007/s11134-009-9136-7.  Google Scholar [9] C. So-In, R. Jain and A.-K. Tamimi, Capacity evaluation for IEEE 802.16e mobile WiMAX,, Journal of Computer Systems, 2010 (2010), 1.  doi: 10.1155/2010/279807.  Google Scholar [10] Standard IEEE 802.16-2009, Part 16: Air Interface for Broadband Wireless Access Systems, Standard for Local and Metropolitan Area Networks,, May 2009., (2009).   Google Scholar [11] H. Takagi, "Analysis of Polling Systems,", MIT Press, (1986).   Google Scholar [12] A. Vinel, Y. Zhang, Q. Ni and A. Lyakhov, Efficient request mechanism usage in IEEE 802.16,, IEEE Global Telecommunications Conference (GLOBECOM), 1 (2006), 1.   Google Scholar
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