This paper investigates a partial-order connection (POC) service/proto
col. Unlike classic transport services that deliver objects either in
the exact order transmitted or according to no particular order, POC p
rovides a partial-order service; that is, a service that requires some
, but not all objects to be received in the order transmitted. Two ver
sions of POC are proposed: reliable, which requires that all transmitt
ed objects are eventually delivered, and unreliable, which permits the
service to lose a subset of the objects. In the unreliable version, o
bjects are more finely categorized into one of three reliability class
es depending on their temporal value. Two metrics based on e(i)(P), th
e number of linear extensions of partial-order P in the presence of i
lost objects, are proposed as complexity measures of different combina
tions of partial order and reliability. Formulae for calculating e(i)(
P) are derived when P is series-parallel. A formal specification of a
POC protocol, written in Estelle, is presented and discussed. This spe
cification was designed and validated using formal description tools a
nd will provide a basis for future implementations.