**8. Application criticality**

The criticality *cr* of an application is defined as,

$$\mathcal{L}\_r(\mathfrak{a}, E) = \frac{\mathfrak{a}}{\psi(E)} \tag{7}$$

which represents the ratio of the weights placed on the empirical benefit and power cost, respectively. At one extreme, *cr*(∞, *E*) allocates maximum resources towards throughput performance, while, at the other extreme, *cr*(0, *E*) emphasizes energy conservation for

#### 14 Wireless Sensor Networks / Book 1 202 Wireless Sensor Networks – Technology and Protocols

*minimum energy routing*. The associated optimized link utility *L*∗ *vx*,*vy*, *<sup>f</sup>* for minimum energy routing is,

$$L^\*\_{v\_{\upsilon}, v\_{y}, f}(r^\*\_{v\_{\upsilon}, v\_{y}, f}, t) = -\psi(E) \xrightarrow{q\_{t\_{\upsilon\_{\upsilon}}} 1} \frac{r^\*\_{v\_{\upsilon}, v\_{y}, f}}{m} \tag{8}$$

where the goal is to minimize the link's power cost. The corresponding objective function is,

*Ua*<sup>∗</sup> *vi*,*vj* (*t*) = *max* 1 *K* − 1 *g* ∑ *x*=1 *L*∗ *vx*,*vx*+1, *fx* (*r*∗ *vx*,*vx*+1, *fx* , *t*) + *K*−1 ∑ *z*=*g*+1 *L*∗ *vz*,*vz*+1, *fz* (*r*∗ *vz*,*vz*+1, *fz* , *t*) *s*.*t*. (1) *Pvx*, *fx* · *Pvx*+1, *fx* = 0, ∀*vx*, *vx*+<sup>1</sup> ∈ *pathvi*,*vj* (2) *Pvz*, *fz* · *Pvz*+1, *fz* = 0, ∀*vz*, *vz*+<sup>1</sup> ∈ *pathvi*,*vj* (3) *Pvx*, *fx* , *Pvz*, *fz* = *max*(*PMIRS*, *PSNR*), ∀*vx*, *vz* ∈ *pathvi*,*vj* (4) *K* ≤ *K*� . (9)

where the effect of minimum energy routing is seen in the third constraint, which enforces that the minimum required power to transmit between node pairs is chosen.

The impact of application criticality on resource allocation will be analyzed by comparing the throughput performance of smart routing versus minimum energy routing.

## **9. Packet formats**

In gathering the required node information for the cross-layer policy, we define the state of a node *vx* that includes:


State information is broadcasted to announce presence in the network and is also used in the propagation of resource allocation to nodes selected during the optimization process using a coordination channel. The state information above and the position of a node are all that a cluster-head requires to optimize a request.

From this point onwards, we shall denote *V* and *M* as the cardinalities of the sensor and mesh nodes sets as *V* = |*Vi*| and *M* = |*Mi*|, respectively, to simplify equations.
