It is common knowledge that the development of transport infrastructure goes on by leaps and bounds today.
>The number of autos grows as the population grows.
>autos
automobiles

>There are a lot of new roads, that are being built right now, also there are new road junctions that has to make stability on transport routes.
>a lot of new roads, that are being built
a lot of new roads being built
>that has to make stability on ... routes
aimed at stabilizing ... routes

In this case, it is very important to make new modernization relevance. [to make ... relevant?]
>So where are traffic lights necessary?
So, where neccessary places for trafic lights are?
Where should we make [dig?] a tunnel and where is it important to build crosswalks?
What is the best way to pave the way to a new community, and improve the road system in the old one?
It depends on the need of all traffic participants. [on every traffic participant's needs]
It is very important to work out and determine model tasks of planning and projecting [designing! projecting is that thing when you apply one to another, or when you use a lightbulb to show shanow theatre] problems that answer the questions of real measuring [measurements?] because of big price ones. [meh? didn't catch that. Because of the big prices at stake? Because every large-scale implementation is costly?]

One of the problems in +++different+++ macroscopic modeling ---different--- tasks is calculation time, that vehicles spend in a way. ["in a way" == "неким образом". Are you a hundred percent sure you didn't want to write 'in transit'?]

In 1952, British scientist John Glen Wardrop [no comma needed here] showed his <<two principles of equilibrium>> to the world. That one pertains to Nash’s concept of equilibrium from the game theory, that had been designed independently from each other. [ЩЬТО.] First principle was almost the same the ideas of Frank Knight, stated in 1920-th. [The first principle is almost identical to ideas Frank Knight first published in 1920s.] Wardrop's first principle states that the journey times in all routes actually used are equal or less than those that would be experienced by a single vehicle on any unused route. Each user non-cooperatively seeks to minimize his cost of transportation. [is there a need in emphasis on this being the interpretation? because I feel cohesion of the text being lost at this point.] The traffic flows that satisfy this principle are usually referred to as <<user equilibrium>> (UE) flows, since each user chooses the route that is the best [in his or her opininon. -- or you may just write '... the best route']. Specifically, a user-optimized equilibrium is reached when no user may lower his transportation cost through unilateral action. If we continue to make physical analogies, then the model of traffic flow will be accurately [hedge that, i.e. 'rather accurately'] described in a model of spread [spread model? (OMG ofs world takeover, everybody take cover in bunkerz lolz)] of a viscous fluid. Wardrop's second principle states that at equilibrium, the average journey time is at a minimum. ['a minimium'? not 'at minimum'? you 100% sure the statement includes the possibility of another minimums somewhere in other point? because if yes, and another minimum points may exist, then leave your text as it is, if not - correct it to 'at minimum'] That implies that all users behave cooperatively in choosing their routes to ensure the most efficient use of the whole system. Wardrop's second principle are generally deemed system optimal (SO).



In 1956 Beckmann, McGuire and Winsten made the mathematician model of net balance, where optimum is equilibrium of Nash-Wardrop.

In 60-th Dietrich Braess found the [not 'the', at this point it's still 'a paradox'] paradox, that in future will be named ---as a--- [you don't say 'который в будущем будет назван как' in Russian, do you?] Braess paradox. He gave the example [an example!] of the transport network, in which the construction of a new road leads to an increase in the overall time costs. This paradox was ---described first time--- +++first described+++ in \cite{Braess_1968} and, in later transcription,  \cite{Braess_2005}.

\begin{figure} [h]
\centering
\includegraphics[width=10cm]{Images/Braessyara}
\caption{Braess Paradox}
\label{fig:braess}
\end{figure}

Let’s describe Braess paradox on +++a+++ real example [no comma needed here] that had been found in Vladivostok (Russia) \cite{Gasnikov}. On the edges of a [an! pure phonetics here, it's VERY easy to remember it correctly : if the next word starts with a vowel sound, you use 'an', if it starts with a consonant sound, you use 'a'. Simple as that. I beg you mention this allows English to flow continiously, and simple understanding of this phonetic rule pushes you forward in pronounciation dramatically. So yeah, remember it well.] oriented transport graph [no comma here] we show depends on time in a way from quantity vehicles on the way [we show the dependency of transit time from the number of vehicles participating in traffic.    You may also take habit of bannning the word 'way' for yourself, cuz it's WAY too ambiguious. Its general meaning is not 'путь', but 'способ' or 'образ', that's why it's not that good. For the traffic artery description, I suggest 'route' or plain 'road', and for the time - you saw it already above - 'transit time']. ---If you describe that in simple words:--- +++In simple words,+++ [это устойчивое] +++here is the story.+++ Firstly [At first], The Airport and the city was connected by two ways. One of them passes [passed; let's align all the tenses here, to seem less a schizophreniac to our reader] through the town Artem and the second one through c. Cherepahi. Both of roads are [were] in bad state and don’t [didn't] have big capacity. In this case, for reasons of simple [for simplicity,] [we let] geometry workload of each road ---is about--- the same. After that[,] a big game zone [big game zone == 'зона для охоты накрупную дичь'. U sure u wrote what u meant?] and [a] highway had been built on c.Cherepahi. Workload of this road grew after that. But it didn’t make a big influence to the distribution of transport routes [it didn't influence the distribution ... much,], as when the highway from Artem to Vladivostok had been built [didn't influence ... as much, as ... ??]. Paradox arose [no comma needed] when the highway Artem-Gameland had been built. When the new road appeared, the equilibrium time path dramatically increased, because of the Nash-Wardrop’s equilibrium [conditions] for this network[. The equilibrium is ]achieved if enough autos [automobiles? or am I being derelict here and noone says automobiles in Europe?] are on way [follow the route] Airport – Gameland – Vladivostok. How is Braess paradox working [The way Braess paradox works] is very similar to <<prisoner’s dilemma>> from [the] game theory. Every participant chose the most optimal strategy for himself[remember, it's 'himself/herself' in English, you dirty sexist maniac] and because of that optimal equilibrium [parameters] become [became] worse.

\begin{figure} [h]
\centering
\includegraphics[width=10cm]{Images/Braess}
\caption{Braess Paradox}
\label{fig:braess}
\end{figure}

Let we [Let us] have intensity of vehicle flow from node 1 to node 4 equal 6 vehicles per [a] time period. Let $y_{ij}$ is [be! The construction here is 'Let ... be the ...', not any other way around! You may think English is similar to C++, but the horrible truth here is everything's vice versa: the C++ is similar to English.] [the] intensity of flow in the edge from the node $i$ to the edge $j$, so at the each edge we have time as [a] function of flow. The user equilibrium can be reached when all the used routes have the same travel time (in another case[,] the drivers [YES! no sexism detected here! I almost anticipated another 'he/she' pitfall.] will choose [the drivers choose; that's to align tenses to the prefix outside of this paretheses.] the shortest route). We have 3 possible routes: $1 \to 3 \to 4$, $1 \to 3 \to 2 \to 4$, $1 \to 2 \to 4$.
If this [these!] 6 vehicles are uniform [uniformly] distributed on this [these!] routes (2 vehicles per time period for each [per each route. Be a good English writer and maintain symmetry. 'per X per Y per Z' is a good balanced symmetrical language construct. Although your 'for each' is plausible, is feels cumbersome here.]), so the time cost for each vehicle will be equal 92 minutes ($10\cdot (2+2) +(50+2) = 10 \cdot(2+2)+(10+2)+10\cdot(2+2) = (50+2)+10\cdot(2+2)$). Such distribution will be единственным [the only; i'd embed Static-X -- The Only here, but this plaintext format does not allow for mp3 embedding :3] Nash-Wardrop’s equilibrium in this network. In means [This means?], than [that?] nobody in this configuration will not change his route at the condition that [will not change his or her route provided that] another drivers save his route [their routes].

Let us close the central edge $3 \to 2$. The [new] configuration with traffic flow equals 3 vehicles per time period at the routes $1 \to 3 \to 4$ и $1 \to 2 \to 4$ stays единственной [Static-X -- The Only] equilibrium. In this configuration the total time for one vehicle will be $10\cdot3+(50+3) = (50+3)+10\cdot 3$ = 83 minutes.


So [remove this 'so' bloodily - it's a parasite word], we have [Thus, it is determined] that if at the initial traffic network we did not have this central road, then it is not need [then there is no need] to build it --- because of other than the costs for the construction of the road [because even disregaring construction costs,], there will be additional time costs arising because of the intersection of this part of town ['из-за пересечения этой части города'? say what again? rewrite it in an understandable way] . Of course, if this [no comma needed] <<subnet>> can not be allocated, as isolated, search problem of inefficient edges is much more complicated [O_o General WTF from this sentence. I request the original Russian.]. In 2001 Roughgarden showed that the search of inefficient edges is [an - phonetic rule exclusion; or not? try saying both 'a AnPee' and 'an AnPee' to understand the choice here.] NP-hard problem \cite{Roughgarden_2006}.
Also in the article of Valiant and Roughgarden from 2006 \cite{Valiant_2006}
was shown than [it was shown that] the probability of the appearance of Braess paradox [] in random graphs when the number of nodes grows up to infinity, approaches to 1.
[*sigh* Also, in the article by Valiant and Roughgarden (2006) it was shown that the probability of Braess paradox emergence approaches 1 when the number of nodes grows up to infinity in random graphs.]


 This paradox was also found [have also been found] in New York when 42nd street was closed in 1990. In Stuttgart, when a new highway was closed [here you need to symmetrize the grammar and add more details - at least, the date of the incident]. In Seoul, South Korea, a speeding up [a speed up?] in traffic around [around or across? if you meant the insides of Seoul, you want 'across', and 'around' otherwise.] the city was seen [was reported?] when a motorway was removed as part of [as part of -> during] the Cheonggyecheon restoration project.