# 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:

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##### References:
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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