# A Cross-Layer Optimization QoS Scheme in Wireless Multimedia Sensor Networks
## 3 Problem Formation and Dynamic Algorithm
### Comparison of Performance  
In the simulation of Figures 1-8, performances of CLADS-BCD, CLADS-MAC, EASYO, and ACH are compared. The initial energy in the sink node, non-real-time nodes, and multimedia nodes were 5 J, 0.5 J, and 2 J, respectively. This simulation lasted for 100,000 time slots. The stability period is defined as the time duration from the establishment of the network to the death of the first node [24]. The stability period is crucial for the applications which require the feedback from the sensor network to be reliable [22]. In Figure 1, the stability periods of different schemes are compared. It can be seen that the stability period of ACH was the longest. The stability period of CLADS-BCD was longer than that of CLADS-MAC and EASYO. Therefore, in backpressure-style schemes, CLADS-BCD makes the network more stable than CLADS-MAC and EASYO. In wireless sensor networks, the energy of the nodes around the sink node can easily be exhausted, which limits the stability periods of WSNs. Under ACH, in each cluster-setup round, the nodes with more residual energy can be chosen as the cluster heads with higher probabilities, and this can balance the energy consumption of nodes around the sink node. Therefore, networks under ACH had the longest stability periods. CLADS-BCD, CLADS-MAC, and EASYO all consider residual energy states of nodes in scheduling to balance energy consumption. In the CLADS schemes, distance coefficients for energy queues are applied to reduce the energy consumption of nodes around the sink node, and this leads to longer stability periods under CLADS-BCD than under EASYO. The reason why the stability periods under CLADS-MAC were the shortest is that CLADS-MAC adoptsa distributed media access control scheme in scheduling, obtaining sub-optimal transmission link sets. The consumed powers of the network under different schemes are compared in Figure 2. Figure 2 shows that the consumed power of the network under cluster-based ACH was the lowest. Figure 2 also shows that the consumed power of the network under CLADS-BCD was lower than those under EASYO and CLADS-MAC. The reason is that TDMA scheduling was adopted in each cluster, which effectively reduces consumed power. Unlike EASYO, in CLADS-BCD, queues were normalized in a Lyapunov function to unify the dimension of the queues, which led to more valid weights of the energy queues in the framework, and a reduction in consumed power. The transmission link sets obtained by the distributed media access control scheme in the scheduling of CLADS-MAC were sub-optimal, and this increased the consumed power of the network. In Figure 3 and Figure 4, the ratios of survival nodes in and out of the region of radius \(R\) are compared, respectively. From Figure 3 and Figure 4, we can see that ACH performed best most of the time. The reason is that under ACH, energy consumption is well balanced, due to the use of clusters. TDMA scheduling is also utilized in clusters to further reduce energy consumption. The ratios of survival nodes both in and out of the region of radius \(R\) under CLADS-BCD were much higher than those under CLADS-MAC and EASYO. This implies that, for back  
Figure 1: Stability period with varying number of nodes. Figure 2: Consumed power of the network with varying number of nodes. the network lifetime under CLADS-BCD is longer than that under EASYO and CLADS-MAC. The reason is as follows. Transmission powers of the nodes around the sink node are reduced through the utilization of distance coefficients for energy queues and distance coefficients for data queues in the CLADS schemes. Therefore, the average lifetime of nodes in the region of radius \(R\) under CLADS-BCD is greatly increased. CLADS also performs better than EASYO in reducing the energy consumption of nodes out of the region of radius \(R\), through applying the normalization of queues in optimization framework. In addition, since CLADS-BCD is optimal and CLADS-MAC is sub-optimal in scheduling, CLADS-BCD performs better than CLADS-MAC.