The above formulation does not take into account any prior information, from for example a previous survey. A seed
matrix can be constructed from a previous survey. While the seed matrix does not necessarily have to satisfy the
observed link flows, the seed matrix can be utilized to expand the maximum likelihood function as shown in Equation 4b.
It can be noted that the likelihood of an individual trip from i to j is tij/ΣΣtij, based on the above seed matrix. Consequently,
the probability of Tij trips being drawn is ( tij/ΣΣtij)Tij. It can be shown, in Figure 2, that the use of the above non-uniform
seed matrix yields a different maximum likelihood O-D matrix with a different objective function. Conversely, when a
uniform seed matrix is applied to the 5-link network of Figure 1, it can be shown to have no impact on the final optimum
O-D solution; however the value of the objective function is different. This finding is unique to only certain network types,
and does not hold in general. For reasons that will be discussed later, it will be considered that the formulation including
the seed is the correct one, when the formulation with and without the seed differ.