American Institute of Mathematical Sciences

Advanced
July  2011, 7(3): 607-622. doi: 10.3934/jimo.2011.7.607

Optimal design and analysis of a two-hop relay network under Rayleigh fading for packet delay minimization

Hong Il Cho 1, and  Gang Uk Hwang 2,

1. 

Department of Mathematical Sciences and Telecommunication Engineering Program, Korea Advanced Institute of Science and Technology, Daejeon, South Korea
2. 

Department of Mathematical Sciences and Telecommunication Engineering Program, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 305-701, South Korea

Received  September 2010 Revised  May 2011 Published  June 2011

In this paper, we consider a wireless network consisting of a source node, a destination node and multiple relay nodes under Rayleigh fading. Cooperative diversity in the network is achieved by selecting an opportunistic relay node with the best channel condition to the destination node. We focus on the packet level performance in this paper and analyze the average packet delay of the network for various modulation and coding schemes. We assume that the arrival process of packets follows a Markov modulated Poisson process (MMPP). To derive the average packet delay, we first derive the distribution of the number of packets that are successfully transmitted from the source node to the destination node via a relay node. Using the distribution obtained above, a queueing process of the M/G/1 type is developed to model the queue at the source node. The average packet delay is then obtained from the stationary distribution of the queueing process of the source node by applying Little's Lemma. Based on our results on the average packet delay, the optimal modulation and coding scheme for given network parameters is determined to minimize the average packet delay. We validate our analytic model through simulation. The detailed relations between the average packet delay and network parameters such as average signal to noise ratios (SNRs) between nodes, the number of relay nodes and packet arrival rate, are investigated through numerical studies based on our analytic model as well as simulation studies. From our numerical results, we conclude that the optimal modulation and coding scheme that minimizes the average packet delay depends not only on SNRs of channels between nodes but also on the arrival rate of packets at the data link layer.
Keywords: Rayleigh fading, Markov modulated Poisson process (MMPP), opportunistic relay selection scheme., Packet delay, relay network.
Mathematics Subject Classification: Primary: 68M10, 68M20; Secondary: 60K2.
Citation: Hong Il Cho, Gang Uk Hwang. Optimal design and analysis of a two-hop relay network under Rayleigh fading for packet delay minimization. Journal of Industrial & Management Optimization, 2011, 7 (3) : 607-622. doi: 10.3934/jimo.2011.7.607
References:
[1]

A. Bletsas, H. Shin and M. Z. Win, Cooperative communication with outage-optimal opportunistic relaying, IEEE Trans. on Wireless Commun., 6 (2007), 3450-3460. doi: 10.1109/TWC.2007.06020050.  Google Scholar

[2]

J. Cai, A. S. Alfa, P. Ren, X. Shen and J. W. Mark, Packet level performance analysis in wireless user-relaying networks, IEEE Trans. on Wireless Commun., 7 (2008), 5336-5345. doi: 10.1109/T-WC.2008.070960.  Google Scholar

[3]

G. Casella and R. L. Berger, "Statistical Inference," 2nd edition, Duxbury, 2001. Google Scholar

[4]

W. Chen, L. Dai, K. B. Letaief and Z. Cao, A unified cross-layer framework for resource allocation in cooperative networks, IEEE Trans. on Wireless Commun., 7 (2008), 3000-3012. doi: 10.1109/TWC.2008.060831.  Google Scholar

[5]

T. M. Cover and A. E. Gamal, Capacity theorems for the relay channel, IEEE Trans. Inform. Theory, 25 (1979), 572-584. doi: 10.1109/TIT.1979.1056084.  Google Scholar

[6]

H. Heffes and D. M. Lucantoni, A Markov modulated characterization of packetized voice and data traffic and related statistical multiplexer performance, IEEE J. on Sel. Areas in Commun., 4 (1986), 856-868. doi: 10.1109/JSAC.1986.1146393.  Google Scholar

[7]

J. N. Laneman and G. W. Wornell, Distributed space-time coded protocols for exploiting cooperative diversity in wireless networks, IEEE Trans. Inform. Theory, 49 (2003), 2415-2425. doi: 10.1109/TIT.2003.817829.  Google Scholar

[8]

Q. Liu, S. Zhou and G. B. Giannakis, Queueing with adaptive modulation and coding over wireless links: Cross-layer analysis and design, IEEE Trans. on Wireless Commun., 4 (2005). Google Scholar

[9]

C. K. Lo, R. W. Heath and S. Vishwanath, The impact of channel feedback on opportunistic relay selection for hybrid-ARQ in wireless networks, IEEE Trans. on Veh. Tech., 58 (2009), 1255-1268. Google Scholar

[10]

M. F. Neuts, "Structured Stochastic Matrices of $M$/$G$/$1$ type and their Applications," Probability: Pure and Applied, 5, Marcel Dekker, Inc., New York, 1989.  Google Scholar

[11]

T. S. Rappaport, "Wireless Communications: Principle and Practice," 2nd edition, Pentice Hall PTR., 2002. Google Scholar

[12]

B. Rong and A. Ephremides, Protocol-level cooperation in wireless networks: Stable throughput and delay analysis, in "Proc. the 7th Intl. Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt)," Seoul, Korea, 2009. Google Scholar

[13]

A. Sendonaris, E. Erkip and B. Aazhang, User cooperation diversity - Part I: System description, IEEE Trans. on Commun., 51 (2003), 1927-1938. doi: 10.1109/TCOMM.2003.818096.  Google Scholar

[14]

H. Y. Wei and R. D. Gitlin, Two-hop-relay architecture for next-generation WWAN/WLAN integration, IEEE Wireless Commun., 11 (2004), 24-30. doi: 10.1109/MWC.2004.1295734.  Google Scholar

[15]

S. Xu and T. Saadawi, Does the IEEE 802.11 MAC protocol work well in multihop wireless Ad Hoc networks?, IEEE Commun. Mag., 39 (2001), 130-137. doi: 10.1109/35.925681.  Google Scholar

[16]

K. Zheng, Y. Wang, L. Lei and W. Wang, Cross-layer queueing analysis on multihop relaying networks with adaptive modulation and coding, IET Commun., 4 (2010), 295-302. doi: 10.1049/iet-com.2009.0380.  Google Scholar

show all references

References:
[1]

A. Bletsas, H. Shin and M. Z. Win, Cooperative communication with outage-optimal opportunistic relaying, IEEE Trans. on Wireless Commun., 6 (2007), 3450-3460. doi: 10.1109/TWC.2007.06020050.  Google Scholar

[2]

J. Cai, A. S. Alfa, P. Ren, X. Shen and J. W. Mark, Packet level performance analysis in wireless user-relaying networks, IEEE Trans. on Wireless Commun., 7 (2008), 5336-5345. doi: 10.1109/T-WC.2008.070960.  Google Scholar

[3]

G. Casella and R. L. Berger, "Statistical Inference," 2nd edition, Duxbury, 2001. Google Scholar

[4]

W. Chen, L. Dai, K. B. Letaief and Z. Cao, A unified cross-layer framework for resource allocation in cooperative networks, IEEE Trans. on Wireless Commun., 7 (2008), 3000-3012. doi: 10.1109/TWC.2008.060831.  Google Scholar

[5]

T. M. Cover and A. E. Gamal, Capacity theorems for the relay channel, IEEE Trans. Inform. Theory, 25 (1979), 572-584. doi: 10.1109/TIT.1979.1056084.  Google Scholar

[6]

H. Heffes and D. M. Lucantoni, A Markov modulated characterization of packetized voice and data traffic and related statistical multiplexer performance, IEEE J. on Sel. Areas in Commun., 4 (1986), 856-868. doi: 10.1109/JSAC.1986.1146393.  Google Scholar

[7]

J. N. Laneman and G. W. Wornell, Distributed space-time coded protocols for exploiting cooperative diversity in wireless networks, IEEE Trans. Inform. Theory, 49 (2003), 2415-2425. doi: 10.1109/TIT.2003.817829.  Google Scholar

[8]

Q. Liu, S. Zhou and G. B. Giannakis, Queueing with adaptive modulation and coding over wireless links: Cross-layer analysis and design, IEEE Trans. on Wireless Commun., 4 (2005). Google Scholar

[9]

C. K. Lo, R. W. Heath and S. Vishwanath, The impact of channel feedback on opportunistic relay selection for hybrid-ARQ in wireless networks, IEEE Trans. on Veh. Tech., 58 (2009), 1255-1268. Google Scholar

[10]

M. F. Neuts, "Structured Stochastic Matrices of $M$/$G$/$1$ type and their Applications," Probability: Pure and Applied, 5, Marcel Dekker, Inc., New York, 1989.  Google Scholar

[11]

T. S. Rappaport, "Wireless Communications: Principle and Practice," 2nd edition, Pentice Hall PTR., 2002. Google Scholar

[12]

B. Rong and A. Ephremides, Protocol-level cooperation in wireless networks: Stable throughput and delay analysis, in "Proc. the 7th Intl. Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt)," Seoul, Korea, 2009. Google Scholar

[13]

A. Sendonaris, E. Erkip and B. Aazhang, User cooperation diversity - Part I: System description, IEEE Trans. on Commun., 51 (2003), 1927-1938. doi: 10.1109/TCOMM.2003.818096.  Google Scholar

[14]

H. Y. Wei and R. D. Gitlin, Two-hop-relay architecture for next-generation WWAN/WLAN integration, IEEE Wireless Commun., 11 (2004), 24-30. doi: 10.1109/MWC.2004.1295734.  Google Scholar

[15]

S. Xu and T. Saadawi, Does the IEEE 802.11 MAC protocol work well in multihop wireless Ad Hoc networks?, IEEE Commun. Mag., 39 (2001), 130-137. doi: 10.1109/35.925681.  Google Scholar

[16]

K. Zheng, Y. Wang, L. Lei and W. Wang, Cross-layer queueing analysis on multihop relaying networks with adaptive modulation and coding, IET Commun., 4 (2010), 295-302. doi: 10.1049/iet-com.2009.0380.  Google Scholar

[1]

Hong Il Cho, Myungwoo Lee, Ganguk Hwang. A cross-layer relay selection scheme of a wireless network with multiple relays under Rayleigh fading. Journal of Industrial & Management Optimization, 2014, 10 (1) : 1-19. doi: 10.3934/jimo.2014.10.1
[2]

Xiaoshuang Xing, Gaofei Sun, Yong Jin, Wenyi Tang, Xiuzhen Cheng. Relay selection based on social relationship prediction and information leakage reduction for mobile social networks. Mathematical Foundations of Computing, 2018, 1 (4) : 369-382. doi: 10.3934/mfc.2018018
[3]

Alain Jacquemard, Weber Flávio Pereira. On periodic orbits of polynomial relay systems. Discrete & Continuous Dynamical Systems, 2007, 17 (2) : 331-347. doi: 10.3934/dcds.2007.17.331
[4]

Linyi Qian, Wei Wang, Rongming Wang. Risk-minimizing portfolio selection for insurance payment processes under a Markov-modulated model. Journal of Industrial & Management Optimization, 2013, 9 (2) : 411-429. doi: 10.3934/jimo.2013.9.411
[5]

Leonid Shaikhet. Stability of delay differential equations with fading stochastic perturbations of the type of white noise and poisson's jumps. Discrete & Continuous Dynamical Systems - B, 2020, 25 (9) : 3651-3657. doi: 10.3934/dcdsb.2020077
[6]

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
[7]

Yoora Kim, Gang Uk Hwang, Hea Sook Park. Feedback limited opportunistic scheduling and admission control for ergodic rate guarantees over Nakagami-$m$ fading channels. Journal of Industrial & Management Optimization, 2009, 5 (3) : 553-567. doi: 10.3934/jimo.2009.5.553
[8]

Fang Han, Bin Zhen, Ying Du, Yanhong Zheng, Marian Wiercigroch. Global Hopf bifurcation analysis of a six-dimensional FitzHugh-Nagumo neural network with delay by a synchronized scheme. Discrete & Continuous Dynamical Systems - B, 2011, 16 (2) : 457-474. doi: 10.3934/dcdsb.2011.16.457
[9]

Wouter Rogiest, Koen De Turck, Koenraad Laevens, Dieter Fiems, Sabine Wittevrongel, Herwig Bruneel. On the optimality of packet-oriented scheduling in photonic switches with delay lines. Numerical Algebra, Control & Optimization, 2011, 1 (4) : 727-747. doi: 10.3934/naco.2011.1.727
[10]

Hyeon Je Cho, Ganguk Hwang. Optimal design for dynamic spectrum access in cognitive radio networks under Rayleigh fading. Journal of Industrial & Management Optimization, 2012, 8 (4) : 821-840. doi: 10.3934/jimo.2012.8.821
[11]

Zsolt Saffer, Miklós Telek, Gábor Horváth. Analysis of Markov-modulated fluid polling systems with gated discipline. Journal of Industrial & Management Optimization, 2021, 17 (2) : 575-599. doi: 10.3934/jimo.2019124
[12]

Marianito R. Rodrigo, Rogemar S. Mamon. Bond pricing formulas for Markov-modulated affine term structure models. Journal of Industrial & Management Optimization, 2021, 17 (5) : 2685-2702. doi: 10.3934/jimo.2020089
[13]

Deena Schmidt, Janet Best, Mark S. Blumberg. Random graph and stochastic process contributions to network dynamics. Conference Publications, 2011, 2011 (Special) : 1279-1288. doi: 10.3934/proc.2011.2011.1279
[14]

Daoyi Xu, Yumei Huang, Zhiguo Yang. Existence theorems for periodic Markov process and stochastic functional differential equations. Discrete & Continuous Dynamical Systems, 2009, 24 (3) : 1005-1023. doi: 10.3934/dcds.2009.24.1005
[15]

Qing-Qing Yang, Wai-Ki Ching, Wanhua He, Tak-Kuen Siu. Pricing vulnerable options under a Markov-modulated jump-diffusion model with fire sales. Journal of Industrial & Management Optimization, 2019, 15 (1) : 293-318. doi: 10.3934/jimo.2018044
[16]

E. Almaraz, A. Gómez-Corral. On SIR-models with Markov-modulated events: Length of an outbreak, total size of the epidemic and number of secondary infections. Discrete & Continuous Dynamical Systems - B, 2018, 23 (6) : 2153-2176. doi: 10.3934/dcdsb.2018229
[17]

Lakhdar Aggoun, Lakdere Benkherouf. A Markov modulated continuous-time capture-recapture population estimation model. Discrete & Continuous Dynamical Systems - B, 2005, 5 (4) : 1057-1075. doi: 10.3934/dcdsb.2005.5.1057
[18]

Gábor Horváth, Zsolt Saffer, Miklós Telek. Queue length analysis of a Markov-modulated vacation queue with dependent arrival and service processes and exhaustive service policy. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1365-1381. doi: 10.3934/jimo.2016077
[19]

Wei Wang, Linyi Qian, Xiaonan Su. Pricing and hedging catastrophe equity put options under a Markov-modulated jump diffusion model. Journal of Industrial & Management Optimization, 2015, 11 (2) : 493-514. doi: 10.3934/jimo.2015.11.493
[20]

Yang Shen, Tak Kuen Siu. Consumption-portfolio optimization and filtering in a hidden Markov-modulated asset price model. Journal of Industrial & Management Optimization, 2017, 13 (1) : 23-46. doi: 10.3934/jimo.2016002

2020 Impact Factor: 1.801

Tools

Metrics

  • PDF downloads (42)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences | Privacy Policy