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

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 λ_min(n) by which the first passage time attains its minimum, is nearly . Our result indicates that time cost of the process in which each node transmits packet with transmission rate λ_min(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.

Qiao WangEmail: