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This shows three tasks, all with the same period. To handle tasks with periods which are multiples of the same lowest period, the scheduler loop or task functions can be modi ed so that they only execute the task every m ticks for some value of m. Alternatively, for more exibility, a major/minor cycle scheme may be employed where the system period is the least common multiple of the periods of all tasks and within each period each task executes several times. In both schemes, problems will be encountered tting tasks into the schedule. Consider the following two tasks: Task 1 runs for 1 ms every 2 ms, deadline 2 ms Task 2 runs for 1.5 ms every 4 ms, deadline 4 ms. It is not possible to execute task 2 continuously for 1.5 ms since then task 1 would miss its deadline. Instead, task 2 must be divided into two pieces, each of which has an execution time <1 ms. These pieces can then be tted into the gaps between invocations of task 1. So you end up with:

categorization, those routing protocols that assume that sensors are aware of their physical coordinates.

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8.3 ROUTING WITH KNOWN POSITIONS When investigating position-based routing algorithms for sensor networks, it is natural to assume the a priori knowledge of location information via preprogramming or GPS-like services. Thus, no efforts are made by these protocols to establish location within a network. Current methods make some necessary assumptions. First, links are bidirectional: If node x can receive messages from node y, then y can receive messages from x. In addition, communication models often adhere to the simple unit disk graph (UDG) model where all communication ranges are normalized to some range r. In the UDG neighbors are pairs of nodes separated by a Euclidean distance r. The UDG model is relaxed later in our discussion. Feasible schemes must, at a minimum, prove to be loop-free and scalable. We demonstrate some of these subtleties by starting with a discussion of the naive approaches to position-based routing. 8.3.1 Naive Forwarding Mechanisms Research into scalable forwarding methods for sensor networks has explored a variety of forwarding schemes. Scalability is maintained by keeping knowledge only of the nodes in communication range and choosing the next hop based on this knowledge. All position-based schemes share a common theme: The next hop is determined by maximizing or minimizing some criteria associated with local nodes positions. We call this the progress criteria. Notions of Progress . We begin with a formal de nition of progress. Say a node s holds a message to be forwarded to a destination location d (see Figure 8.2) and has knowledge of all node locations within its communication radius. Then we

void main() { wait_for_next_tick(); ++tick_count; do_task1(); if (tick_count & 1) do_task2_second_half(); else do_task2_first_half(); }

; Mills, R G Ef cacy and safety of the oral neuraminidase inhibitor oseltamivir in treating acute in uenza: a randomised controlled trial US Oral Neuraminidase Study Group JAMA 2000, 283, 1016 1024 42 Whitley, R J; Hayden, F G; et al Oral oseltamivir treatment of in uenza in children Pediatr Infect Dis J 2001, 20, 127 133 43 Gubareva, L V; Webster, R G; Hayden, F G Detection of in uenza virus resistance to neuraminidase inhibitors by an enzyme inhibition assay Antiviral Res 2002, 53, 47 61 44 Mulder, J; Hers, J F In uenza Wolters-Noordhoff Publishing, Groningen, 1972 45 Opie, E I; Blake, F G; Small, J C; Rivers, T M In Epidemic Respiratory Disease: The Pneumonia and Other Infections of the Respiratory Tract Accompanying In uenza and Measles Kimpton H, London, 1921, p402 46 Winternitz, M.

have the following de nition used to better understand the behavior of position-based forwarding schemes De nition 831 The progress of a node x en route from sender s to destination d is de ned as the orthogonal projection of the location of x onto the line sd We use Figure 82 to better demonstrate various notions of progress as discussed below In this gure, sensor node s holds a message destined for sensor node d The large circle centered at s represents the communication range of s; thus all nodes inside the circle are neighbors of s The dotted horizontal line sd is the line onto which orthogonal projections are made in order to evaluate and compare progress criteria The rst forwarding mechanism based on the idea of progress was proposed by Takagi and Kleinrock [14].

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