The smooth traffic flow, which refers to the stochastically stabilized flow (ie. flow without disruption, that prevents the acceptance of a specific probability distribution of the headways), in the queuing model with moving buffer, can be described using the maximum density referring to the smooth flow.
In smooth flow vehicles ride with the speed with no additional delays (no waiting time), and with the same intensity of vehicles by all minimal distances that are components of path of the smooth flow. The density stands for the jam density and therefore is length of elementary segments of the road, as described for example in the queuing model with moving buffer. Thus is the maximal number of vehicles forming smooth flow. The gap between vehicles in smooth traffic flow —taking place on the road consisting of distances — is dependent on the expected (mean) speed of free traffic flow and shall take into consideration the safety distance (safe gap), mapped by shifting the exponential distribution of headways on the road. Such mapping is also related to the fact that in description of the traffic flows of high density the small variances of gaps are taken into account. In addition, in dense traffic flows a minimal safety distance (safe gap) is relatively small, with the result that the probability of disruption—in the form of sudden deceleration (stop) of vehicles—increases. Therefore, the probability (risk) of the formation of queues of vehicles is growing. 
Intelligent Transportation Systems (ITS) are interrelated systems that work together to deliver transportation ITS services . An ITS architecture defines a framework within which ITS systems can be built, and the information that is exchanged between elements of ITS systems, as :
Mentioning above ITS systems offer the potential to improve smoothness of traffic flows, by means of the user services grouped in service packages . Therefore for modelling of expected traffic smoothness that takes into account ITS user services and services packages the specific description of ITS systems is required.
The average delays—which correspond to the traffic flow passing through the elements of transportation network—are closely dependent on the speed, density, and intensity both of the analyzed traffic flow and of other flows in the network - flows interact at each elementary node. It should also be noted that the values of these three fundamental characteristics of traffic flow for each elementary node may be different. Average delay which corresponds to the passing of the traffic flow through any elementary node by applying package of the ITS services, is dependent on traffic conditions in the node.
Determination of the relationship between the smoothness and the intensity of traffic flows leads to the optimization problem of traffic assignment in the transportation network. According to the optimal traffic assignment in the transportation network is conditioned by optimization of traffic assignment in each elementary node of the network. Only the analysis of elementary traffic conflicts in the nodes provides an accurate assessment of the smoothness of traffic flows. Disruptions of the smoothness of the traffic flows usually occur in the critical nodes. So, on the one hand disturbed traffic flow indicates the location of the greatest potential benefits from the improvement of traffic assignment, and on the other – the structure of the queues in the complex critical nodes maps the reserve capacity in their elementary nodes. This allows for such selection of the package of the ITS services, that leads to the optimal variant of the traffic assignment.
The permanent small disruptions are the results of very high density of traffic flow. They are caused by gaps between vehicles that are close to minimal distances (minimal gaps) - the variation of the gaps is equal to or close to zero. In such situation the high probability (risk) of the formation of queues is caused by delayed reaction of human-vehicle system. The probability of disruption, resulting in the queues of vehicles, increases nonlinearly with increasing of the intensity and of the density of the traffic flows. In a similar way, the waiting time in the queue of vehicles is increasing, if such disruption has occurred. In addition, the smaller the conditional capacity is—and thus the smaller optimal intensity, due to the low level of smoothness of traffic flows—the faster the waiting time in the queue due to disruption is growing. Therefore the optimal intensities for the individual network elements are not equal to their capacities - they are smaller. This follows from the fact that the intensity of the traffic flow equal capacity of the node occurs when all vehicles are moving in the states close to the saturation states with very limited levels of service, and thus the function of the expected smoothness of traffic flow reaches zero - no vehicle is moving freely.
The assumptions about the smoothness of traffic flow, may be supplemented by the postulated way of describing the traffic conditions in congested transportation networks. In such networks, with dense traffic flows and a high risk of the disruption (even in the form of a short queue of vehicles) the probability of such an incident seems to be a better measure of the probabilistic description of the capacity constraints than the expected waiting time in the queue, because the probability takes into account the risk of delay in the traffic flow from the point of view of the person that plans a trip.
That is particularly important in congested networks, in which a high probability of queues is most often associated with high expected value of extension of travel time - as a result of the high risk of the large number of secondary disruptions and queues because of a sequence of following forms of congestion: the single interaction -> the multiple interaction -> bottleneck -> triggerneck -> gridlock.
Mtiririko laini trafiki, ambayo inahusu mtiririko stochastically imara (yaani. Mtiririko wa maji bila kuvunjika, ambayo inazuia kukubalika kwa usambazaji maalum wa uwezekano wa headways, katika mfano wa kuandamana na buffer inayoendelea, inaweza kuelezwa kwa kutumia wiani wa juu unaohusu mtiririko laini. Katika mtiririko laini, magari husafiri kwa kasi bila kuchelewesha zaidi (hakuna wakati wa kusubiri), na kwa nguvu sawa na magari kwa umbali wote mdogo ambao ni sehemu ya njia ya mtiririko laini. Kiasi cha jams ni kiasi cha jams, na kwa hiyo ni urefu wa sehemu za msingi za barabara, kama ilivyoelezwa kwa mfano katika mfano wa kuandamana na buffer ya kusonga. Hivyo ni idadi ya juu ya magari kuunda mtiririko laini. Pengo kati ya magari katika mtiririko la trafiki laini <unk>kuchukua nafasi juu ya barabara inayojumuisha umbali <unk> inategemea inatarajiwa (kati) kasi ya mtiririko wa trafiki huru na lazima kuzingatia umbali wa usalama (pengo la usalama), ramani kwa kuhamisha usambazaji exponential ya headways juu ya barabara. Ramani kama hiyo pia inahusiana na ukweli kwamba katika maelezo ya mtiririko wa trafiki wa wiani wa juu tofauti ndogo za mapungufu zinafikiriwa. Aidha, katika mtiririko wa trafiki dense umbali wa chini wa usalama (upungufu wa usalama) ni ndogo kwa kulinganisha, na matokeo yake kwamba uwezekano wa usumbufu - katika fomu ya kasi ya ghafla (kusimamisha) ya magari - huongezeka. Kwa hiyo, uwezekano (hatari) ya malezi ya foleni ya magari ni kuongezeka. Intelligent Transportation Systems (ITS) ni mfumo wa usafiri unaohusiana ambao hufanya kazi pamoja ili kutoa huduma za usafiri. ITS ni mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo wa mfumo. Kwa hiyo, kwa ajili ya modeling ya matarajio ya usafiri laini ambayo inachukua huduma za watumiaji ITS na huduma pakiti, maelezo maalum ya ITS mifumo inahitajika. wastani ucheleweshaji - ambayo inalingana na mtiririko wa trafiki kupita kupitia vipengele vya mtandao wa usafiri - ni karibu kutegemea kasi, wiani, na nguvu wote wa kuchambuliwa mtiririko wa trafiki na ya mtiririko mwingine katika mtandao - mtiririko kuingiliana katika kila msingi node. Ni lazima pia kumbuka kwamba maadili ya hizi tatu msingi sifa ya mtiririko wa trafiki kwa kila msingi node inaweza kuwa tofauti. Wakati wa wastani wa kuchelewa unaolingana na kupita kwa mtiririko wa trafiki kupitia node yoyote ya msingi kwa kutumia pakiti ya huduma za ITS, inategemea hali ya trafiki katika node. Uamuzi wa uhusiano kati ya smoothness na nguvu ya mtiririko wa trafiki inaongoza kwa tatizo optimization ya utoaji trafiki katika mtandao wa usafiri. Kulingana na optimum trafiki utoaji katika mtandao wa usafiri ni hali na optimization ya trafiki utoaji katika kila msingi node ya mtandao. Tu uchambuzi wa migogoro ya msingi ya trafiki katika nodes hutoa tathmini sahihi ya usawa wa mtiririko wa trafiki. Kuvurugwa kwa usawa wa mtiririko wa trafiki kawaida hutokea katika nodes muhimu. Hivyo, kwa upande mmoja kusumbuliwa trafiki mtiririko inaonyesha eneo la faida kubwa ya uwezekano kutoka kwa kuboresha trafiki utoaji, na kwa upande mwingine <unk> muundo wa foleni katika nodes tata muhimu ramani uwezo wa akiba katika nodes yao ya msingi. Hii inaruhusu kwa ajili ya uteuzi huo wa mfuko wa huduma ITS, ambayo inaongoza kwa toleo bora ya utoaji trafiki. Vizuizi vidogo vya kudumu ni matokeo ya wiani wa juu sana wa mtiririko wa trafiki. Wao ni unasababishwa na mapungufu kati ya magari ambayo ni karibu na umbali mdogo (mapungufu madogo) - tofauti ya mapungufu ni sawa na au karibu na sifuri. Katika hali kama hiyo uwezekano mkubwa (hatari) ya malezi ya foleni ni unasababishwa na kucheleweshwa athari ya binadamu-gari mfumo. Uwezekano wa usumbufu, na kusababisha foleni ya magari, huongezeka nonlinearly na kuongezeka kwa nguvu na wiani wa mtiririko wa trafiki. Kwa njia sawa, muda wa kusubiri katika foleni ya magari ni kuongezeka, kama kuvurugika kama hiyo imetokea. Aidha, ndogo uwezo masharti ni <unk> na hivyo ndogo ya ufanisi nguvu, kutokana na kiwango cha chini cha laini ya mtiririko wa trafiki <unk> kwa kasi muda wa kusubiri katika foleni kutokana na usumbufu ni kukua. Kwa hiyo nguvu bora kwa ajili ya vipengele vya mtandao binafsi si sawa na uwezo wao - wao ni ndogo. Hii inatokana na ukweli kwamba nguvu ya mtiririko wa trafiki sawa na uwezo wa node hutokea wakati magari yote yanaenda katika hali karibu na hali ya saturation na viwango vya huduma vya chini sana, na hivyo kazi ya usawa wa trafiki inakaribia sifuri - hakuna gari linaloenda kwa uhuru. Dhana kuhusu smoothness ya mtiririko wa trafiki, inaweza kuongezwa na njia postulated ya kuelezea hali ya trafiki katika mitandao ya usafiri congested. Katika mitandao kama hiyo, na mtiririko wa trafiki na hatari kubwa ya usumbufu (hata katika fomu ya foleni fupi ya magari), uwezekano wa tukio kama hilo unaonekana kuwa kipimo bora cha maelezo ya uwezekano wa vikwazo vya uwezo kuliko muda wa kusubiri katika foleni, kwa sababu uwezekano unachukua hatari ya kuchelewesha kwa mtiririko wa trafiki kutoka kwa mtazamo wa mtu anayepanga safari. Hii ni muhimu hasa katika mitandao congested, ambapo uwezekano mkubwa wa foleni ni mara nyingi kuhusishwa na thamani ya juu ya matarajio ya upanuzi wa muda wa kusafiri - kama matokeo ya hatari kubwa ya idadi kubwa ya kuvuruga sekondari na foleni kwa sababu ya mfululizo wa aina zifuatazo za congestion: moja mwingiliano, nyingi mwingiliano, bottleneck, gridlock.