  This paper constructs an h-model structure for diagrams of streams, locally
preordered spaces. Along the way, the paper extends some classical
characterizations of Hurewicz fibrations and closed Hurewicz cofibrations. The
usual characterization of classical closed Hurewicz cofibrations as inclusions
of neighborhood deformation retracts extends. A characterization of classical
Hurewicz fibrations as algebras over a pointed Moore cocylinder endofunctor
also extends. An immediate consequence is a long exact sequence for directed
homotopy monoids, with applications to safety verifications for database
protocols.
