# American Institute of Mathematical Sciences

July  2011, 7(3): 717-733. doi: 10.3934/jimo.2011.7.717

## Performance evaluation of a power saving mechanism in IEEE 802.16 wireless MANs with bi-directional traffic

 1 College of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China 2 Department of Intelligence and Informatics, Konan University, Kobe 658-8501

Received  September 2010 Revised  May 2011 Published  June 2011

One of the most important ways for extending the battery lifetime of Mobile Stations (MSs) in a wireless Metropolitan Area Network (MAN) is to conserve the power consumption effectively. When a power saving mechanism with the sleep mode in IEEE 802.16-2009 is used, the system will be in a sleep state and the energy will be saved if both the Uplink (UL) and the Downlink (DL) are idle. In this paper, we present a new mathematical analysis for the system model with synchronous multiple vacations to capture the working principle of the Power Saving Class (PSC) type III in IEEE 802.16-2009 by taking into account the bi-directional traffic (the UL traffic and DL traffic together). By using the methods of a semi-Markov process and a two-dimensional embedded Markov chain, we derive the steady-state probability distribution of the system. Noting that the transmission of UL data frame will not be influenced by the sleep mode, but the sleep mode can be terminated by the arrival of UL data frames, we give the formula for the average delay of the DL data frames taking the bi-directional traffic into consideration. Moreover, we also present the expression for the energy saving ratio. Analytical results and simulation results are provided to investigate and validate the influence of the system parameters on the system performance. Finally, considering the trade-off between the average delay of data frames and the energy saving ratio, we develop a cost function to determine the optimal length of the sleep window in order to maximize the energy saving ratio while satisfying the Quality of Service (QoS) constraint on the average delay of data frames.
Citation: Shunfu Jin, Wuyi Yue, Xuena Yan. Performance evaluation of a power saving mechanism in IEEE 802.16 wireless MANs with bi-directional traffic. Journal of Industrial & Management Optimization, 2011, 7 (3) : 717-733. doi: 10.3934/jimo.2011.7.717
##### References:

show all references

##### References:
 [1] Zhanqiang Huo, Wuyi Yue, Naishuo Tian, Shunfu Jin. Performance evaluation for the sleep mode in the IEEE 802.16e based on a queueing model with close-down time and multiple vacations. Journal of Industrial & Management Optimization, 2009, 5 (3) : 511-524. doi: 10.3934/jimo.2009.5.511 [2] Sangkyu Baek, Bong Dae Choi. Performance of an efficient sleep mode operation for IEEE 802.16m. Journal of Industrial & Management Optimization, 2011, 7 (3) : 623-639. doi: 10.3934/jimo.2011.7.623 [3] Zsolt Saffer, Miklós Telek. Analysis of BMAP vacation queue and its application to IEEE 802.16e sleep mode. Journal of Industrial & Management Optimization, 2010, 6 (3) : 661-690. doi: 10.3934/jimo.2010.6.661 [4] Shunfu Jin, Wuyi Yue. Performance analysis and evaluation for power saving class type III in IEEE 802.16e network. Journal of Industrial & Management Optimization, 2010, 6 (3) : 691-708. doi: 10.3934/jimo.2010.6.691 [5] 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 [6] Qiuli Liu, Xiaolong Zou. A risk minimization problem for finite horizon semi-Markov decision processes with loss rates. Journal of Dynamics & Games, 2018, 5 (2) : 143-163. doi: 10.3934/jdg.2018009 [7] Zhe Zhang, Jiuping Xu. Bi-level multiple mode resource-constrained project scheduling problems under hybrid uncertainty. Journal of Industrial & Management Optimization, 2016, 12 (2) : 565-593. doi: 10.3934/jimo.2016.12.565 [8] Ramon Quintanilla, Reinhard Racke. Stability in thermoelasticity of type III. Discrete & Continuous Dynamical Systems - B, 2003, 3 (3) : 383-400. doi: 10.3934/dcdsb.2003.3.383 [9] Seung-Yeal Ha, Yongduck Kim, Zhuchun Li. Asymptotic synchronous behavior of Kuramoto type models with frustrations. Networks & Heterogeneous Media, 2014, 9 (1) : 33-64. doi: 10.3934/nhm.2014.9.33 [10] Zsolt Saffer, Wuyi Yue. M/M/c multiple synchronous vacation model with gated discipline. Journal of Industrial & Management Optimization, 2012, 8 (4) : 939-968. doi: 10.3934/jimo.2012.8.939 [11] Kyung Jae Kim, Jin Soo Park, Bong Dae Choi. Admission control scheme of extended rtPS algorithm for VoIP service in IEEE 802.16e with adaptive modulation and coding. Journal of Industrial & Management Optimization, 2010, 6 (3) : 641-660. doi: 10.3934/jimo.2010.6.641 [12] Shengzhu Jin, Bong Dae Choi, Doo Seop Eom. Performance analysis of binary exponential backoff MAC protocol for cognitive radio in the IEEE 802.16e/m network. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1483-1494. doi: 10.3934/jimo.2017003 [13] Dequan Yue, Jun Yu, Wuyi Yue. A Markovian queue with two heterogeneous servers and multiple vacations. Journal of Industrial & Management Optimization, 2009, 5 (3) : 453-465. doi: 10.3934/jimo.2009.5.453 [14] Xiangying Meng, Gemma Huguet, John Rinzel. Type III excitability, slope sensitivity and coincidence detection. Discrete & Continuous Dynamical Systems - A, 2012, 32 (8) : 2729-2757. doi: 10.3934/dcds.2012.32.2729 [15] Sangkyu Baek, Bong Dae Choi. Performance analysis of power save mode in IEEE 802.11 infrastructure wireless local area network. Journal of Industrial & Management Optimization, 2009, 5 (3) : 481-492. doi: 10.3934/jimo.2009.5.481 [16] Zhuangyi Liu, Ramón Quintanilla. Energy decay rate of a mixed type II and type III thermoelastic system. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1433-1444. doi: 10.3934/dcdsb.2010.14.1433 [17] Cheng-Dar Liou. Optimization analysis of the machine repair problem with multiple vacations and working breakdowns. Journal of Industrial & Management Optimization, 2015, 11 (1) : 83-104. doi: 10.3934/jimo.2015.11.83 [18] Chia-Huang Wu, Kuo-Hsiung Wang, Jau-Chuan Ke, Jyh-Bin Ke. A heuristic algorithm for the optimization of M/M/$s$ queue with multiple working vacations. Journal of Industrial & Management Optimization, 2012, 8 (1) : 1-17. doi: 10.3934/jimo.2012.8.1 [19] Ramon Quintanilla. Structural stability and continuous dependence of solutions of thermoelasticity of type III. Discrete & Continuous Dynamical Systems - B, 2001, 1 (4) : 463-470. doi: 10.3934/dcdsb.2001.1.463 [20] Filippo Dell'Oro, Vittorino Pata. Memory relaxation of type III thermoelastic extensible beams and Berger plates. Evolution Equations & Control Theory, 2012, 1 (2) : 251-270. doi: 10.3934/eect.2012.1.251

2018 Impact Factor: 1.025