## 3 Proposed Approach
### Discussion of Simple Heuristic Approaches that seem Obvious
However, it can be performed using derivatives evaluation of the information loss intensity function (8):  
\[\frac{\partial E}{\partial x}=\lim_{x\to 0}\frac{Loss(x+\Delta x)-Loss(x)}{ \Delta x}, \tag{8}\]  
where \(Loss(x)\) is the intensity of losses in the channel, under the condition that \(x\) units of information/sec. are delivered. The physical meaning of this value is as follows: it allows estimating the increased amount of information loss when adding an information flow, \(\Delta x\) (units per second). In fact, the two streams are compared according to the criterion of minimum losses. This allows us to state the optimality of using the channel for which the derivative of losses in stream has the smallest value. This conclusion is of great importance and will be used further in this study. At the same time, finding the value of the function \(Loss(x)\) in analytical form is impossible, so there is pseudo-code in the algorithm for finding \(Loss(x)\) using the numerical method (Algorithm 3). ```
1 Required: \(\mu\): channel bandwidth capacity, \(N\): size of the channel buffer, \(Q\): intensity of the information flow that must reach the output. 2 Assign \(k=0\). // iteration number
3 Assign \(e>0\). // stopping criterion
4 Assign \(p_{\max}\). //second stopping criterion
5 Assign \(p^{(k)}=0\). // estimated probability of losses at the current iteration
6 Start an endless loop: 1. Calculate \(x^{(k)}=\frac{Q}{(1-p^{(k)})}\). // intensity of the information flow sent to the input (based on the estimated probability of losses) 2. Calculate \(p^{(k+1)}=p(x^{(k)},\mu,N)\). // real probability of losses at the current iteration 3. If \(\left|p^{(k+1)}-p^{(k)}\right|<e\), then STOP and return the pair \(\{flag=1;x_{rez}=x^{(k+1)}\}\). // the algorithm has converged, there is a solution 4. If \(p^{(k+1)}>p_{\max}\), then STOP and return the pair \(\{flag=0;x_{rez}=None\}\). // the algorithm does not converge, and there is no solution 5. If none of the criteria are satisfied, then set \(k=k+1\) and move on to the next iteration of the loop. Figure 2: Dependence of channel bandwidth capacity on changes in the intensity of information loss. Blue curve—the 1 st channel, red curve—the 2 nd channel. ### Estimating Partial Derivatives

The dependence of variables on the probability of losses for the entire telecommunication network in accordance with changes of information flow at any edge of its graph by the value \(\Delta x\) are under study. Let us consider the network shown in Figure 3.

The figure shows three routes connecting nodes: 1-2-4-5 (green arrows), 2-4-6-8 (brown arrows), 3-4-6-7 (blue arrows). It is necessary to increase the data transfer rate for the information flow in the channel from the 6 th node to the 7 th by the amount \(\Delta x_{67}\). It is obvious that the probability of \(p_{67}\) loss has also increased. Since a certain amount of information is delivered along the route highlighted in blue (Figure 3), the incoming information flow to the 6 th node must be increased by a certain amount, \(\Delta x_{46}\), in order to compensate for the increase in the probability of information flow losses. An increase in the channel load from the sixth node to the seventh node will lead to an increase in the load from the fourth node to the sixth node. Obviously, this, in turn, increases the load on the channel from the 3 rd to the 4 th nodes. Analysis of the data shows that the load has increased along the entire route up to the seventh node, which is highlighted in blue. This leads to increased losses along the route highlighted in red in the channel from the fourth to the sixth node. These losses need to be compensated, so the load on the channel increases from the second node to the fourth node. Therefore, there are losses in the information flow along the route highlighted in green, which also need to be compensated.