THEORETICAL BASIS OF A FLOW-TRAVEL TIME RELATIONSHIP FOR USE IN TRANSPORTATION PLANNING.

The flow-travel time relationship, first proposed in 1966, has been found to have all the required characteristics of such a relationship; however, beyond a loose association with queueing theory, no adequate theoretical basis had been found. This paper demonstrates that the relationship can be derived from either of two queueing models, both of which assume the road operates as a specific number of sequential queueing elements. In one model the delay parameter J is the proportion of elements which cause delay and in the other it has a close association with the Erlang number. This association is explored and comments on practical use of the relationship are made.