  The current paper deals with the subject of shortest path routing in
transportation networks (in terms of travelling time), where the speed in
several of the network's roads is a function of the time interval. The main
contribution of the paper is a procedure that is faster compared to the
conventional approaches, that derives the road's traversal time according to
the time instant of departure, for the case where the road's speed has a
constant value inside each time interval (in general, different value for each
time interval). Furthermore, the case where the road's speed is a linear
function of time inside each time interval (in general, different linear
function for each time interval) is investigated. A procedure that derives the
road's traversal time according to the time instant of departure is proposed
for this case as well. The proposed procedures are combined with Dijkstra's
algorithm and the resulting algorithms, that are practically applicable and of
low complexity, provide optimal shortest path routing in the networks under
investigation.
