Abstract
In this paper, we study the performance of Slotted ALOHA in an elementary process in wireless sensor networks, in which sensors are activated by rare events and transmit packets to a single sink node within single hop. The time cost of the process can be viewed as a first passage time and we give the expectation of time and energy cost which is dependent on both the size of active nodes and their transmission rate by a first passage time analysis. Meanwhile, given the size of active nodes n, we demonstrated that the optimal transmission rate λmin(n) by which the first passage time attains its minimum, is nearly \({\sqrt{\log n}/n}\) . Our result indicates that time cost of the process in which each node transmits packet with transmission rate λmin(n) increases nearly linearly with n increasing. We present the maximum likelihood estimate (MLE) of the size of active nodes from the viewpoint of sink nodes so that activated nodes can adjust its transmission rate to improve the performance of the process. Energy dissipation and time cost of the procedure in the channel model of Multi Packet Reception (MPR) are considered also. Numerical results indicate that both time cost and energy consumption of the procedure in MPR channel is superior to that in Single Packet Reception (SPR) channel while the transmission rate near or less than the optimal values with which time costs attain their minimum. Otherwise the energy dissipation in MPR channel is more than that in SPR channel although comparison of time cost in the above two channels reveals the superiority of MPR channel.
Similar content being viewed by others
References
Abramson, N. (1970). The ALOHA system—another alternative for computer communications. In Proceedings of Fall Joint Computer Conference, 1970.
Sameer T., Abu-Ghazaleh N.B., Heinzelman and W. (2002). A taxonomy of wireless micro-sensor network models. ACM SIGMOBILE Mobile Computing and Communications Review 6(2): 28–36
Rangarajan, H., & Garcia-Luna-Aceves, J. J. (2004). Reliable data delivery in event-driven wireless sensor networks. In Proceedings of Ninth International Symposium on Computers and Communications, 2004.
Motegi, S., Yoshihara, K., & Horiuchi, H. (2004). Implementation and evaluation of on-demand address allocation for event-driven sensor network. In Processing of Intelligent Sensors, Sensor Networks and Information Conference, 2004.
Xu, N., & Cassandras, C. G. (2006). Dynamic sleep time control in event-driven wireless sensor networks. In Proceedings of the 45th IEEE Conference on Decision and Control, 2006.
Roberts, L. (1972). Aloha packet system with and without slots and capture. Tech. Rep., Stanford Res. Inst., Advanced Research Projects Agency, Network Information Center, Stanford, CA, 1972.
Abramson N. (1977). The throughput of packet broadcasting channels. IEEE Transactions on Communications 25(1): 117–128
Abramson, N. (1973). Packet switching with satellites. In Proceedings of AFIPS Conference, 1973.
Bertsekas, D., & Gallager, R. (1987). Data Networks (2nd Ed.) Saddle River, New Jersey 07458: Prentice Hall.
Gallager R. (1985). A perspective on multiaccess channels. IEEE Transactions on information Theory 31(2): 124–142
Tsybakov B. and Mikhailov W. (1979). Ergodicity of slotted ALOHA system. Problemy Peredachi Informassi 15: 73–87
Rao R. and Ephremides A. (1988). On the stability of interacting queues in a multiple-access system. IEEE Transactions on Information Theory 34(5): 918–930
Szpankowski W. (1994). Stability conditions for some distributed systems: Buffered random access systems. Advances in Applied Probability 26: 498–515
Bachelier, L. (1900). Annales des Sciences de l’Ecole Superieure, 21, 17
Smoluchowski, M. V. (1915). Physikalische Zeitschrift, 16, 318.
Darling, D. A., & Siegert, A. J. F. (1953). Annals Mathematical Statistics, 24, 624.
Weiss G.H. (1977). Stochastic processes in chemical physics. MIT Press, Cambridge
Gardiner C.W. (1997). Handbook of stochastic methods. Springer-Verlag, Berlin
Tuckwell H.C. (1988). Introduction to theoretical neurobiology. Cambridge University Press, Cambridge
Rangarajan G. and Ding M.Z. (2000). First passage time problem for biased continuous-time random walks. Fractals 8(2): 139–145
Ghez S., Verd S. and Schwartz S. (1988). Stability properties of Slotted ALOHA with multipacket reception capability. IEEE Transactions on Automatic Control 33(7): 640–649
Ghez S., Verd S. and Schwartz S. (1989). Optimal decentralized control in the random-access multipacket channel. IEEE Transactions on Automatic Control 33(11): 1153–1163
Sant J. and Sharma V. (2000). Performance analysis of a Slotted-ALOHA protocol on a capture channel with fading. Queuing System, Theory and Application 34(1): 1–35
Naware V., Mergen G. and Tong L. (2005). Stability and delay of finite-user Slotted ALOHA with multipacket reception. IEEE Transactions on Information Theory 51(7): 2636–2656
Angel, G. D., & Fine, T. L. (2000). Randomized power control strategies for optimization of multiple access radio systems. Proc. 38th Allerton Conf. Communication, Control and Computing, Oct. 2000.
Habbab I.M.I. et al (1989). ALOHA with capture over slow and fast fading radio channels with coding and diversity. IEEE Journal on Selected Areas Communications 7: 79–88
Vanderplas C. and Linnartz J.P.M. (1990). Stability of mobile Slotted ALOHA network with Rayleigh fading, shadowing and near-far effect. IEEE Transactions on Vehicular Technologgy 39: 359–366
Zorzi M. and Rao R.R. (1994). Capture and retransmission control in mobile radio. IEEE Journal on Selected Areas in Communications 12: 1289–1298
Lo, F. L., Ng, T. S., & Yuk, T. I. (2000). Delay-throughput comparison of single and multi-channel slotted ALOHA networks. In proceedings of International Conference on Communication Technology, 2000.
IEEE Computer Society LAN/MAN Standards Committee. IEEE Standard 802.15.4. (2003). The Institute of Electrical and Electronics Engineers, 2003.
Mergen G. and Tong L. (2002). Random scheduling medium access for wireless ad hoc networks. IEEE 51(7): 868–872
Bougard, B., Catthoor, F., et al. (2005). Energy efficiency of the IEEE 802.15.4 standard in dense wireless microsensor networks: Modeling and improvement perspectives. In Proceedings of the Design, Automation and Test in Europe Conference and Exhibition, 2005.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yu, L., Wang, Q. First Passage Time Analysis in Wireless Sensor Networks for SPR and MPR Systems. Wireless Pers Commun 48, 531–550 (2009). https://doi.org/10.1007/s11277-008-9537-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11277-008-9537-7