The uncertainty inherent in the distributed environment poses new chal
lenges to the efficient utilization of system resources in managing da
tabase transactions. In response to this realization, the execution of
a join query in a system with probabilistic resource and cost paramet
ers is contemplated, leading to the development of stochastic programm
ing models. Information in the form of relational tables and scattered
amongst the sites of a distributed database system is to be collated
and presented to the appropriate user, in response to an issued reques
t. Performing this task demands the usage of limited resources; the ul
timate goal is the determination of an execution strategy incurring mi
nimal cost to the system. The actual state of any network component at
the moment of its exploitation cannot be exactly ascertained in advan
ce. Any interrogation of a distant element must be communicated by the
network, and this involves a delay, as perceived by the questioner, d
uring which the state of the system may change. Indeed, the time at wh
ich a task assigned to any particular component cannot itself be preci
sely predicted, even if the future state of the component could be kno
wn definitively. By considering the uncertain nature of the distribute
d environment, the earlier model of join query evaluation presented in
[1] can be modified in different ways to account for system parameter
s known only in a stochastic sense. This new level of subjectivity is
a revelation of the many different attitudes that may be taken towards
the chance of infeasibility in the solution, for the major issue in d
ealing with uncertainty is the choice of an appropriate measure of ris
k.