In the heterogeneous sensor network, due to the burst and random error, there are the transmission delay, convergence delay, the upstream and the downstream delay etc. because of the burst and random error, as shown in Fig. 1. In this model, the sensor nodes are controlled independently and the signals are received or transmitted according to the change of environment. The coordinator is driven by the session requirement. Convergence nodes are often in periodic operation state or transient dormancy state. In a dormant period, the coordinator can be activated by a session or a server request. The bit error rate is random and burst. The bit error rate affects the data flow between the coordinator and the sensor. The bit error affects the data flow between the sensor and the sink node. The transmission delay is the network delay between coordinator and sensor. The convergence delay is the network delay between the sensor and the sink node. The uplink communication delay between the sink node and the server is the uplink delay. Downlink delay is the delay of the controller and the sink node.
Assuming that network error will not result in the packet error. In a continuous network operating cycle T, a linear description of the network system is shown in Eq. 1.
$$ \left\{\begin{array}{l}x(t)={C}_O(t)x+{C}_G(t)x+{C}_T(t)x\\ {}\tau ={a}_1{\tau}_{TD}+{a}_2{\tau}_{CD}+{a}_3{\tau}_{DLD}+{a}_4{\tau}_{ULD}\\ {}1={a}_1+{a}_2+{a}_3+{a}_4\\ {}\tau \in \left[\begin{array}{cc}\hfill \alpha T,\hfill & \hfill \beta T\hfill \end{array}\right]\end{array}\right. $$
(1)
In Eq. 1, we use the coordinate signal matrix X (T) CO, the convergence signal matrix CG (T) x, and the control signal matrix CT (T) x computing network using the signal sequence x (t). We can obtain the system network delay according to the weight coefficient a1, a2, a3 and a4. Here, τ
TD
is transmission delay. τ
CD
is delay said protector. τ
DLD
is downlink delay. τ
ULD
is uplink delay. In order to maintain the consistency of network delay and the nature of signal attenuation, the sum of a1, a2, a3, and a4 must be 1. α is the lower weight of the working cycle of the network delay. β is the upper bound weight for the work cycle of network delay.
In heterogeneous networks, (1) x (T) is synchronized with the distributed feedback. Further enhancement of the linear properties of heterogeneous networks, as shown in Eq. 2.
$$ \left\{\begin{array}{l}x\left(\tau t\right)={e}^{\alpha +\beta }x(t)+f(t)\\ {}f(t)={\displaystyle \underset{\alpha T}{\overset{\beta T}{\int }}{e}^{\beta T+\tau}\left({C}_O(t)+{C}_G(t)+{C}_T(t)\right)d\tau}\end{array}\right. $$
(2)
In the optimization Eqs. 1 and 2, the delay model of the heterogeneous network is evolved into a closed loop system. Heterogeneous network time delay control logic matrix C
L
(τ) is as shown in Eq. 3.
$$ {C}_L\left(\tau \right)=\left[\begin{array}{ccc}\hfill \varphi \left(\tau \right)+{\displaystyle \sum_{i=1}^Ng\left({t}_i\right){\tau}_i}\hfill & \hfill \alpha {\displaystyle \sum_{i=1}^Ng\left({t}_i\right){\tau}_i}\hfill & \hfill \alpha \hfill \\ {}\hfill \varphi \left(\tau \right)\hfill & \hfill \varphi \left(\tau \right)\hfill & \hfill \varphi \left(\tau \right)\hfill \\ {}\hfill {\displaystyle \sum_{i=1}^Ng\left({t}_i\right){\tau}_i}\hfill & \hfill \beta {\displaystyle \sum_{i=1}^Ng\left({t}_i\right)}\hfill & \hfill \beta {\displaystyle \sum_{i=1}^N{\tau}_i}\hfill \end{array}\right] $$
(3)
Here, φ(τ) denotes the network latency control overhead. N is the number of signal samples. g(t
i
) denotes the closed loop feedback weight.
When the error caused the packet error or loss, the packet loss constraints would be carried out. The improvement of Fig. 2 structure are shown in Fig. 2.
Heterogeneous networks take the controller as the core. The real-time processing of data packet dropout is met by the connection and closing of the constraint logic switch. If the data packet loss, the control logic would send φ(τ) and \( \sum_{i=1}^Ng\left({t}_i\right) \) to delay module. The delay module sends the control signal to the control module. The constraint logic module switches on the updated control logic. Based on data stream C
L
(τ), the controller can get the bit error rate and packet loss rate. If data packet is lost in transmission process, the controller cannot obtain directly the measured values. Only through the constraint module, the reliability maybe guaranteed. The matrix C
L
(τ) of formula (3) would be the \( {\overline{C}}_L\left(\tau \right) \) of formula (4) after the packet loss constraint.
Equation 3 shows the matrix C
L
(τ) of Eq. 4 after the packet loss constraint.
$$ {\overline{C}}_L\left(\tau \right)=\left[\begin{array}{ccc}\hfill 0\hfill & \hfill {\displaystyle \sum_{i=1}^Ng\left({t}_i\right){\tau}_i}\hfill & \hfill {C}_{ST}\hfill \\ {}\hfill {\displaystyle \int \varphi \left(\tau \right)d\tau}\hfill & \hfill {C}_{ST}\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill {C}_{ST}{\displaystyle \int \varphi \left(\tau \right)d\tau}\hfill & \hfill 0\hfill \end{array}\right] $$
(4)
Here, CST is the data packet loss constraint weight.
In the heterogeneous network transmission process, through the collaboration coordinator and controller, the combination of network delay and data packet dropout, delayed constrained data flow, and transport and network distributed rate provide accurate and reliable network architecture.
