First Passage Time Analysis in Wireless Sensor Networks for SPR and MPR Systems

  • Authors:
  • Lu Yu;Qiao Wang

  • Affiliations:
  • School of Information Science and Engineering, Southeast University, Nanjing, China 210096;School of Information Science and Engineering, Southeast University, Nanjing, China 210096

  • Venue:
  • Wireless Personal Communications: An International Journal
  • Year:
  • 2009

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Abstract

In this paper, we study the performance of Slotted ALOHA in anelementary process in wireless sensor networks, in which sensorsare activated by rare events and transmit packets to a single sinknode within single hop. The time cost of the process can be viewedas a first passage time and we give the expectation of time andenergy cost which is dependent on both the size of active nodes andtheir transmission rate by a first passage time analysis.Meanwhile, given the size of active nodes n, wedemonstrated that the optimal transmission rateλmin(n) by which the first passage timeattains its minimum, is nearly $${\sqrt{\log n}/n}$$. Our resultindicates that time cost of the process in which each nodetransmits packet with transmission rateλmin(n) increases nearly linearly withn increasing. We present the maximum likelihood estimate(MLE) of the size of active nodes from the viewpoint of sink nodesso that activated nodes can adjust its transmission rate to improvethe performance of the process. Energy dissipation and time cost ofthe procedure in the channel model of Multi Packet Reception (MPR)are considered also. Numerical results indicate that both time costand energy consumption of the procedure in MPR channel is superiorto that in Single Packet Reception (SPR) channel while thetransmission rate near or less than the optimal values with whichtime costs attain their minimum. Otherwise the energy dissipationin MPR channel is more than that in SPR channel although comparisonof time cost in the above two channels reveals the superiority ofMPR channel.