There is no simple answer to your question.

I would ask why do you want to "estimate" the flows

what data are available ? 

I want to estimated the road exposure to potential instability phenomena in terms of traffic amount. I evaluated it qualitatively as function of population of two or more urban centers connected by each road stretches. I would like to use a procedure more rigorous.

Not sufficient to reply to you !

Reminds me of several "network safety performance indicator" studies...

https://www.researchgate.net/publication/254860348_En_route_to_safer_roads_how_road_structure_and_road_classification_can_affect_road_safety

https://www.researchgate.net/publication/233994513_Road_safety_performance_indicators_for_the_interurban_road_network

https://www.researchgate.net/publication/304728220_Portuguese_mainland_road_network_safety_performance_indicator

Article En route to safer roads : how road structure and road classi...

Article Road safety performance indicators for the interurban road network

Conference Paper Portuguese mainland road network safety performance indicator

What data are available to yo?. Unless you want to make a survey !

Hi Roberta,

If you want a simple model to calculate traffic volume on road segments connecting several towns and you have only the population data, you can use the Gravity model. It is not a precise model (aggregate model) and does not take into account key variables. However, it is based on the premise that as the population between two nodes increases so does the traffic flow between them. The distance between nodes is another factor. I think you might look at the Four-Step traffic assignment process (trip generation, trip distribution, modal choice and finally route choice (trip assignment).

Dear Roberta

I agree worth Mr. Hamed. 'The Gravity Model' may help you. It is based on Newton's Law which states that two bodies attract themselves with a pull which is proportional to their masses and inversely proportional to the distance between them, and it is an old tool but still used today albeit its application is not straight forward because the distance between two cities is elevated to a coefficient that has to be determined by calibration. Another factors also apply, for instance growth rate of each city in the link,  and traveller behaviour.

There is another model called 'Model of the intervening opportunities', based in that traffic between A and B varies according to increasing or decreasing opportunities in both ends.

There is recent literature on the gravity model, for instance Hong, I and Jung (2016) 'Application of the gravity model on the Korean urban bus network' , W-S in 'Physica A: Statistical Mechanics and its Applications'.Volume 462, 15 November 2016, Pages 48–55

Good luck

 I agree with Mohammad. You may want to look at this short tutorial:

http://www.its.uci.edu/its/publications/papers/CASA/UCI-ITS-AS-WP-07-2.pdf

One useful added feature that is overlooked in the above: if you estimate (as suggested by the gravity model) some level of interaction between the nodes, you still have to assign the traffic to the network. Luckily for you your network seems to be linear with some towns along it so there is a unique (single) way to go between towns. This is a feature of your problem that you can exploit, and importantly it is not a feature of an arbitrary network with many alternative routes. So all you have to do get the flow on Link A is to add all the flows between all pairs of towns that have impact on Link A (perhaps being careful with each direction too!)

        1--------------2----------------3------------4--------------5

            A -->             B-->              C-->              D-->

So A from (1 to 2) would have flows from 1 to 2, plus 1 to 3, plus 1 to 4, plus 1 to 5

etc

Given a street network, a majority of traffic (at least 60%, up to 80% and more) can be accounted by the underlying topological structure. Also top 10% streets account for 90% of all traffic, so called street hierarchy; see details in these papers

https://www.researchgate.net/publication/271830989_Self-organized_natural_roads_for_predicting_traffic_ow_a_sensitivity_study

https://www.researchgate.net/publication/1910404_Street_Hierarchies_A_Minority_of_Streets_Account_for_A_Majority_of_Traffic_Flow

Article Self-organized Natural Roads for Predicting Traffic Flow: A ...

Article Street Hierarchies: A Minority of Streets Account for A Majo...

Many thanks to everybody for very useful suggestions. I'll try to apply the Gravity Model to my road network, that isn't linear (below the map), as assumed by Dr. O'Kelly.

OK -- with a network such as this, you are going to have to model a "path" from I to J .... probably a shortest path would be a good place to start. (There are more complicated ways to do this too of course.) The flow on link A is then the sum of all interaction pairs (OD pairs) that use that link.There is a formula for the volume on link A:

V_a = SUM_ij Tij (Pija)

where Pija = 1 if link a is used on the path from I to J and zero otherwise.

and Tij is your gravity model estimate of the flow from I to J. Probably have to do some work to scale these so the numbers are related to the real world flows that you expect to see. I could see this being useful to you to prioritize the links from busiest to least busy, without necessarily knowing the exact daily volume.

Basically  i feel to carry out peak hour survey on the all the stretch of road is the best method to know the traffic volume on each roads. Though it is time consuming  but will give reliable ranking to all the roads. Bcoz its not neccesary that highly populated places will have maximum trips generated. Videography  survey will only give reliable results

I agree with Mt. Dawda.

It has a great advantage; once you have the surveys done you can use those reliable  values  to calibrate the gravity model by determining the distance exponent

Another vote for Dawda here.

Dear Roberta

You should go once through traditional four step modelling. After finding the number of trips between each urban area by using gravity model and making network of only provincial roads you can find the number of vehicles per each link by assigning the trips on the provincial road network, you can do the trip assignment by some kind of software like TransCAD or JICA Strada.