The ‘best‐fitting’ distance decay parameters were subsequently selected. These decay factors have been fine‐tuned over a period of 10 years. Annual application and interaction with industry have proven the accuracy of these decay factors to model commodity‐flow behavior. These decay factors were utilized as a starting point, informed by known rail and port flows in India, and fine‐tuned through iterative application of the gravity model. However, the freight flow behavior of some commodities in South Africa is completely different to in India, such as sugar cane, which is transported very short distances in South Africa to one region, but long distances across the country in India. The best‐fitting decay factors were used based upon multiple tests of various decay factors to determine the best overall fit in line with partially known data and inputs from local stakeholders.

The UK Department for Transport (2002) also stated that, lacking freight‐flow data from which to estimate the parameters, developers iteratively adjust the coefficients to match observed counts and vehicle miles of travel estimates by truck type and if not available, using analyst judgement. A distance‐ decay parameter is developed for each commodity group individually to account for the varying nature and utility of the commodity, as discussed above.

The gravity modeling is done using software called FlowMap® which was developed in 1990 at Utrecht University. The cost‐effective and user‐friendly software was initially targeted towards use in developing countries’ spatial planning and has been applied successfully in South Africa for various spatial planning purposes since 2000, when the Professional Edition was released. FlowMap® expands typical GIS functionality to allow for the management and analysis of data that depict spatial relations such as distances, flows, travel times and travel costs (Utrecht University, 2013).

The convergence criterion must also be set in FlowMap®. This determines how well the number of trips that to be estimated from the origins and to the destinations has to equal the set variables for the origin and destination constraints respectively. The convergence criterion also determines how well the MTL that is to be estimated has to equal the distance as was set above (de Jong and Van der Vaart, 2010). This is the required accuracy of fit between the modeled data results and the input parameters.

# **<u>Typologies</u>**

Once freight flows have been modeled, they are aggregated to facilitate analysis and recommendations. A succinct view of national freight flows can be obtained through aggregation into two key freight‐flow typologies for India, each with unique transportation characteristics. Firstly, corridor flows occur over long distances between major cities. Due to the high freight density on corridors, these flows provide ideal opportunities for economies of scale and consolidation. Rail transportation is generally the most efficient and suited mode for this type of flow, although countries with navigable river systems (such as some countries in Europe) have had major successes in returning high‐volume freight to inland waterways (Inland Navigation Europe, 2016). Secondly, there are those flows that are neither urban nor corridor flows and are labeled ‘other’. Typified by broad distributions of origins and destinations outside the cities, medium to long distances and low freight densities, flows of this nature are the most difficult to optimize and can be suited to either road or rail (these flows are mainly in rural areas).<sup>2</sup>

> 2 A third typology, urban freight flows (freight traveling within major cities), typically travel short distances, and are more affected by congestion and therefore better suited to smaller road vehicles. Due to the nature of demand‐side modeling, the latter is not modeled, as urban freight mostly refers to the ”last leg” of transport, in effect a double‐count of traffic that has already been measured as a supply‐and‐demand flow, and includes collections, deliveries, distributions and redistributions.

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