# American Institute of Mathematical Sciences

April  2019, 15(2): 739-756. doi: 10.3934/jimo.2018068

## Selection of DRX scheme for voice traffic in LTE-A networks: Markov modeling and performance analysis

 Department of Mathematics, IIT Delhi, New Delhi 110016, India

* Corresponding author: Selvamuthu Dharmaraja

Received  August 2016 Revised  November 2017 Published  June 2018

Power saving is a leading issue in the User Equipment (UE) for limited source of power in Long Term Evolution-Advanced (LTE-A) networks. Battery power of an UE gets exhaust quickly due to the heavy use of many service applications and large data transmission. Discontinuous reception (DRX) is a mechanism used for power saving in UE in the LTE-A networks. There are scope of improvements in conventional DRX scheme in LTE-A networks for voice communication. In this paper, a DRX scheme is chosen by selecting optimal parameters of DRX scheme, while keeping Quality of Service (QoS) delay requirements. Further, delay analysis for first downlink packet is performed. Moreover, expressions for delay distribution and expected delay of any downlink packet, are obtained and represented graphically. Based on analytical model, the trade-off relationship between the power saving and queueing delay is investigated.

Citation: Anupam Gautam, Selvamuthu Dharmaraja. Selection of DRX scheme for voice traffic in LTE-A networks: Markov modeling and performance analysis. Journal of Industrial & Management Optimization, 2019, 15 (2) : 739-756. doi: 10.3934/jimo.2018068
##### References:
 [1] S. Baek and B. D. Choi, Analysis of discontinuous reception (DRX) with both downlink and uplink packet arrivals in 3GPP LTE, In Proceedings of the 6th International Conference on Queueing Theory and Network Applications, (2011), 8–16. [2] S. Baek and B. D. Choi, Analysis of discontinuous reception with both downlink and uplink packet arrivals in 3GPP LTE, Journal of Industrial and Management Optimization, 8 (2012), 841-860. doi: 10.3934/jimo.2012.8.841. [3] P. T. Brady, A model for generating on-off speech patterns in two-way conversation, Bell System Technical Journal, 48 (1969), 2445-2472. [4] T. K. Cheng, J. L. C. Wu, F. M. Yang and J. S. Leu, IEEE 802.16 e/m energy-efficient sleep-mode operation with delay limitation in multibroadcast services, International Journal of Communication Systems, 27 (2014), 45-67. [5] S. Flower, R. S. Bhamber and A. Mellouk, Analysis of adjustable and fixed DRX mechanism for power saving in LTE/LTE-Advanced, In Proceedings of IEEE International Conference on Communications (ICC), (2012), 1964–1969. [6] H. Heffes and D. Lucantoni, A Markov modulated characterization of packetized voice and data traffic and related statistical multiplexer performance, IEEE Journal on Selected Areas in Communications, 4 (1986), 856-868. [7] J. Huang, F. Qian, A. Gerber, Z. M. Mao, S. Sen and O. Spatscheck, A close examination of performance and power characteristics of 4G LTE networks, In Proceedings of the 10th International Conference on Mobile Systems, Applications, and Services, (2012), 225-238. [8] E. Hwang, Y. H. Lee, K. J. Kim, J. J. Son and B. D. Choi, Performance analysis of power saving mechanism employing both sleep mode and idle mode in IEEE 802.16 e, IEICE Transactions on Communications, 92 (2009), 2809-2822. [9] E. Hwang, K. J. Kim, J. J. Son and B. D. Choi, The power-saving mechanism with periodic traffic indications in the IEEE 802.16 e/m, IEEE Transactions on Vehicular Technology, 59 (2010), 319-334. [10] E. Hwang, K. J. Kim and B. D. Choi, Performance Analysis of Power Saving Class of Type Ⅰ for Voice Service in Two-Way Communication in IEEE 802.16 e, IEICE Transactions on Communications, 95 (2012), 845-856. [11] M. J. Karam and F. A. Tobagi, Analysis of the delay and jitter of voice traffic over the internet, In Proceedings of IEEE Twentieth Annual Joint Conference of The IEEE Computer and Communications Societies(ICCS), 2 (2001), 824–833. [12] L. Kong, G. K. W. Wong and D. H. K. Tsang, Performance study and system optimization on sleep mode operation in IEEE 802.16 e, IEEE Transactions on Wireless Communications, 8 (2009), 4518-4528. [13] Y. Y. Mihov, K. M. Kassev and B. P. Tsankov, Analysis and performance evaluation of the DRX mechanism for power saving in LTE, In Proceedings of IEEE 26th Convention of In Electrical and Electronics Engineers in Israel (IEEEI), (2014), 520–524. [14] Rumney and Moray, LTE and the Evolution to 4G Wireless: Design and Measurement Challenges, John Wiley & Sons, 2014. [15] G. Stea and A. Virdis, A Comprehensive Simulation Analysis of LTE Discontinuous Reception (DRX), Computer Networks, 73 (2014), 22-40. doi: 10.1016/j.comnet.2014.07.014. [16] H. P. Stern, S. A. Mahmoud and K. K. Wong, A model for generating on-off patterns in conversational speech, including short silence gaps and the effects of interaction between parties, IEEE Transactions on Vehicular Technology, 43 (1994), 1094-1100. [17] Y. Xiao, Energy saving mechanism in the IEEE 802.16 e wireless MAN, IEEE Communications Letters, 9 (2005), 595-597. [18] Y. Xiao, Performance analysis of an energy saving mechanism in the IEEE 802. 16 e wireless MAN, In Proceedings of 3rd IEEE In Consumer Communications and Networking Conference (CCNC), (2006), 406–410. [19] C. C. Yang, J. Y. Chen, Y. T. Mai and H. H. Liu, Integrated power saving for relay node and user equipment in LTE-A, International Journal of Communication Systems, 29 (2016), 1342-1364. [20] F. Zarai, K. B. Ali, M. S. Obaidat and L. Kamoun, Adaptive call admission control in 3GPP LTE networks, International Journal of Communication Systems, 27 (2014), 1522-1534. [21] Y. Zhang, Y. Xiao and V. C. M. Leung, Energy management analysis and enhancement in IEEE 802.16 e WirelessMAN, IEEE Transactions on Vehicular Technology, 58 (2009), 3738-3752. [22] L. Zhou, H. Xu, H. Tian, Y. Gao, L. Du and L. Chen, Performance analysis of power saving mechanism with adjustable DRX cycles in 3GPP LTE, In Proceedings of IEEE 68th Vehicular Technology Conference, (2008), 1–5. [23] F. Zhu, W. Yiqun and Z. Niu, Delay analysis for sleep-based power saving mechanisms with downlink and uplink traffic, IEEE Communications Letters, 13 (2009), 615-617.

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##### References:
 [1] S. Baek and B. D. Choi, Analysis of discontinuous reception (DRX) with both downlink and uplink packet arrivals in 3GPP LTE, In Proceedings of the 6th International Conference on Queueing Theory and Network Applications, (2011), 8–16. [2] S. Baek and B. D. Choi, Analysis of discontinuous reception with both downlink and uplink packet arrivals in 3GPP LTE, Journal of Industrial and Management Optimization, 8 (2012), 841-860. doi: 10.3934/jimo.2012.8.841. [3] P. T. Brady, A model for generating on-off speech patterns in two-way conversation, Bell System Technical Journal, 48 (1969), 2445-2472. [4] T. K. Cheng, J. L. C. Wu, F. M. Yang and J. S. Leu, IEEE 802.16 e/m energy-efficient sleep-mode operation with delay limitation in multibroadcast services, International Journal of Communication Systems, 27 (2014), 45-67. [5] S. Flower, R. S. Bhamber and A. Mellouk, Analysis of adjustable and fixed DRX mechanism for power saving in LTE/LTE-Advanced, In Proceedings of IEEE International Conference on Communications (ICC), (2012), 1964–1969. [6] H. Heffes and D. Lucantoni, A Markov modulated characterization of packetized voice and data traffic and related statistical multiplexer performance, IEEE Journal on Selected Areas in Communications, 4 (1986), 856-868. [7] J. Huang, F. Qian, A. Gerber, Z. M. Mao, S. Sen and O. Spatscheck, A close examination of performance and power characteristics of 4G LTE networks, In Proceedings of the 10th International Conference on Mobile Systems, Applications, and Services, (2012), 225-238. [8] E. Hwang, Y. H. Lee, K. J. Kim, J. J. Son and B. D. Choi, Performance analysis of power saving mechanism employing both sleep mode and idle mode in IEEE 802.16 e, IEICE Transactions on Communications, 92 (2009), 2809-2822. [9] E. Hwang, K. J. Kim, J. J. Son and B. D. Choi, The power-saving mechanism with periodic traffic indications in the IEEE 802.16 e/m, IEEE Transactions on Vehicular Technology, 59 (2010), 319-334. [10] E. Hwang, K. J. Kim and B. D. Choi, Performance Analysis of Power Saving Class of Type Ⅰ for Voice Service in Two-Way Communication in IEEE 802.16 e, IEICE Transactions on Communications, 95 (2012), 845-856. [11] M. J. Karam and F. A. Tobagi, Analysis of the delay and jitter of voice traffic over the internet, In Proceedings of IEEE Twentieth Annual Joint Conference of The IEEE Computer and Communications Societies(ICCS), 2 (2001), 824–833. [12] L. Kong, G. K. W. Wong and D. H. K. Tsang, Performance study and system optimization on sleep mode operation in IEEE 802.16 e, IEEE Transactions on Wireless Communications, 8 (2009), 4518-4528. [13] Y. Y. Mihov, K. M. Kassev and B. P. Tsankov, Analysis and performance evaluation of the DRX mechanism for power saving in LTE, In Proceedings of IEEE 26th Convention of In Electrical and Electronics Engineers in Israel (IEEEI), (2014), 520–524. [14] Rumney and Moray, LTE and the Evolution to 4G Wireless: Design and Measurement Challenges, John Wiley & Sons, 2014. [15] G. Stea and A. Virdis, A Comprehensive Simulation Analysis of LTE Discontinuous Reception (DRX), Computer Networks, 73 (2014), 22-40. doi: 10.1016/j.comnet.2014.07.014. [16] H. P. Stern, S. A. Mahmoud and K. K. Wong, A model for generating on-off patterns in conversational speech, including short silence gaps and the effects of interaction between parties, IEEE Transactions on Vehicular Technology, 43 (1994), 1094-1100. [17] Y. Xiao, Energy saving mechanism in the IEEE 802.16 e wireless MAN, IEEE Communications Letters, 9 (2005), 595-597. [18] Y. Xiao, Performance analysis of an energy saving mechanism in the IEEE 802. 16 e wireless MAN, In Proceedings of 3rd IEEE In Consumer Communications and Networking Conference (CCNC), (2006), 406–410. [19] C. C. Yang, J. Y. Chen, Y. T. Mai and H. H. Liu, Integrated power saving for relay node and user equipment in LTE-A, International Journal of Communication Systems, 29 (2016), 1342-1364. [20] F. Zarai, K. B. Ali, M. S. Obaidat and L. Kamoun, Adaptive call admission control in 3GPP LTE networks, International Journal of Communication Systems, 27 (2014), 1522-1534. [21] Y. Zhang, Y. Xiao and V. C. M. Leung, Energy management analysis and enhancement in IEEE 802.16 e WirelessMAN, IEEE Transactions on Vehicular Technology, 58 (2009), 3738-3752. [22] L. Zhou, H. Xu, H. Tian, Y. Gao, L. Du and L. Chen, Performance analysis of power saving mechanism with adjustable DRX cycles in 3GPP LTE, In Proceedings of IEEE 68th Vehicular Technology Conference, (2008), 1–5. [23] F. Zhu, W. Yiqun and Z. Niu, Delay analysis for sleep-based power saving mechanisms with downlink and uplink traffic, IEEE Communications Letters, 13 (2009), 615-617.
Basic structure of DRX scheme
One-way communication ON-OFF model for voice traffic
State transition diagram for two-way communication
Packet arrival in one-way communication voice traffic
Frame structure and DRX cycle in LTE-A networks
When sleep period is terminated by a packet
Trade-off between expected delay and time
List of transition rates per second
 $\alpha_{1,4}$ $\alpha_{1,7}$ $\alpha_{3,1}$ $\alpha_{2,1}$ $\alpha_{7,1}$ $\alpha_{4,1}$ $\alpha_{5,1}$ $\alpha_{1,2}$, $\alpha_{7,2}$ $\alpha_{6,5}$ $\alpha_{6,8}$ $\alpha_{2,6}$ $\alpha_{3,6}$ $\alpha_{8,6}$ $\alpha_{5,6}$ $\alpha_{4,6}$ $\alpha_{6,3}$, $\alpha_{8,3}$ $0.833$ $5.489$ $2.157$ $2.324$ $27.62$ $2.222$ $1.044$ $~0.278$
 $\alpha_{1,4}$ $\alpha_{1,7}$ $\alpha_{3,1}$ $\alpha_{2,1}$ $\alpha_{7,1}$ $\alpha_{4,1}$ $\alpha_{5,1}$ $\alpha_{1,2}$, $\alpha_{7,2}$ $\alpha_{6,5}$ $\alpha_{6,8}$ $\alpha_{2,6}$ $\alpha_{3,6}$ $\alpha_{8,6}$ $\alpha_{5,6}$ $\alpha_{4,6}$ $\alpha_{6,3}$, $\alpha_{8,3}$ $0.833$ $5.489$ $2.157$ $2.324$ $27.62$ $2.222$ $1.044$ $~0.278$
Parameters in DRX Scheme
 Parameters Details Half frame Duration (ms) $5$ Duplexing TDD cDRX ON duration timer (ms) $1$ DRX inactivity timer period (ms) $0-100$ Short DRX cycle length (ms) $20$ Long DRX cycle length (ms) $40-100$ Average silence period (ms) (in one-way communication) $650$ Average talking period (ms)(in one-way communication) $350$ Power consumption in awake mode (mJ/ms) $0.24$ Power consumption in sleep mode (mJ/ms) $0.02$ Additional energy consumption(${\mu}J$) $0.2$
 Parameters Details Half frame Duration (ms) $5$ Duplexing TDD cDRX ON duration timer (ms) $1$ DRX inactivity timer period (ms) $0-100$ Short DRX cycle length (ms) $20$ Long DRX cycle length (ms) $40-100$ Average silence period (ms) (in one-way communication) $650$ Average talking period (ms)(in one-way communication) $350$ Power consumption in awake mode (mJ/ms) $0.24$ Power consumption in sleep mode (mJ/ms) $0.02$ Additional energy consumption(${\mu}J$) $0.2$
Number of sleep cycles exhausted in state $S_i$
 $\tau_{1}$ $\tau_{2}$ $\tau_{4}$ $\tau_{7}$ $\tau_{6}$ $\tau_{3}$ $\tau_{5}$ $\tau_{8}$ $7$ $11$ $6$ $0$
 $\tau_{1}$ $\tau_{2}$ $\tau_{4}$ $\tau_{7}$ $\tau_{6}$ $\tau_{3}$ $\tau_{5}$ $\tau_{8}$ $7$ $11$ $6$ $0$
Limiting probabilities
 $\pi_{1}$ $\pi_{2}$ $\pi_{4}$ $\pi_{7}$ $\pi_{6}$ $\pi_{3}$ $\pi_{5}$ $\pi_{8}$ $0.3289$ $0.0236$ $0.0839$ $0.06472$
 $\pi_{1}$ $\pi_{2}$ $\pi_{4}$ $\pi_{7}$ $\pi_{6}$ $\pi_{3}$ $\pi_{5}$ $\pi_{8}$ $0.3289$ $0.0236$ $0.0839$ $0.06472$
Power saving percentage comparison for DRX scheme in one-way and two-way voice
 Length of Long DRX cycle(ms) One-way $P_{0}$$(\%) Two-way P_{L}$$~(\%)$ $40$ $81.96$ $74.78$ $60$ $84.31$ $75.0041$ $80$ $85.75$ $75.12$ $100$ $86.72$ $75.19$
 Length of Long DRX cycle(ms) One-way $P_{0}$$(\%) Two-way P_{L}$$~(\%)$ $40$ $81.96$ $74.78$ $60$ $84.31$ $75.0041$ $80$ $85.75$ $75.12$ $100$ $86.72$ $75.19$
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