**3. Exhaustive-gated two-level polling system**

It can be seen from **Figures 2** and **3**, the performance indicators of the polling systems with three different service policies, i.e., the average queue length and the average waiting delay are different. The average queue length of the exhaustive service polling system is the smallest, the gated service polling system takes the second place, and the average queue length of the limited service polling system is the largest, and the average waiting delay also satisfies the same law. From the perspective of fairness, on the contrary, the fairness of the limited service polling system is the best, while that of the exhaustive service polling system is the worst. The polling systems with three different service strategies have their own characteristics and advantages. In the actual situation, the appropriate polling service strategy should be selected according to the scope of application and application conditions to meet different application needs. When the system requires high fairness, select the limited service strategy; when the system requires high real-time performance, choose the exhaustive service strategy; when the system requires both

real-time and fairness, choose the gated service strategy.

*Wireless Sensor Networks - Design, Deployment and Applications*

*Relationship between average queue length and arrival rate.*

*Relationship between average waiting delay and arrival rate.*

**Figure 2.**

**Figure 3.**

**178**

Based on the basic polling system and the requirements of different priority business in WSNs, an exhaustive-gated two-level polling access control strategy is proposed. The principle of the exhaustive-gated service two-level control polling system is as follows: the polling system is composed of *N* ordinary sites and a central site h. The server serves the central site according to the exhaustive service rule and the ordinary sites according to the gated service rule. The system model is shown in **Figure 4**. After the polling starts, the server first provides exhaustive service to the central site, i.e., the information arrived before the start of the service and the information arrived during the service until the site is empty, and then go to query the ordinary sites. If the ordinary site *i* is not empty, the server will serve it according to the gated service rule. When the service of the site *i* is finished, it will turn to query the central site h. After the central site completes the prescribed service, it starts to serve the ordinary site *i* + 1 again. The exhaustive-gated twolevel control polling system distinguishes between the central site and the ordinary sites by always giving priority to the central site, and the service of the central site is guaranteed first.

We use the methods of stochastic process and probability generating function to analyze the performance of the system. The random variable *ξi*ð Þ *n* is defined as the number of information packets queued for service in the memory of the site *i* at the *tn* time. *ξh*ð Þ *n* is the number of information packets queued for service in the memory of the central station at *tn* time. The state variable of the whole system at *tn* time is f g *ξ*1ð Þ *n* , *ξ*2ð Þ *n* , ⋯, *ξi*ð Þ *n* , ⋯, *ξN*ð Þ *n* , *ξh*ð Þ *n* ; at *tn* <sup>∗</sup> time, the state of the system is f g *ξ*1ð Þ *n* ∗ , *ξ*2ð Þ *n* ∗ … *ξN*ð Þ *n* ∗ , *ξh*ð Þ *n* ∗ . At *tn*þ<sup>1</sup> time, the state of the whole system can be expressed as f g *ξ*1ð Þ *n* þ 1 , *ξ*2ð Þ *n* þ 1 … *ξN*ð Þ *n* þ 1 , *ξh*ð Þ *n* þ 1 . Then the *N* + 1 states of the system constitute a Markov chain, which is aperiodic and ergodic.

**Figure 4.** *Two-level polling system model.*
