<s>
Stochastic	B-Algorithm
scheduling	I-Algorithm
concerns	O
scheduling	B-Application
problems	O
involving	O
random	O
attributes	O
,	O
such	O
as	O
random	O
processing	O
times	O
,	O
random	O
due	O
dates	O
,	O
random	O
weights	O
,	O
and	O
stochastic	O
machine	O
breakdowns	O
.	O
</s>
<s>
The	O
objective	O
of	O
the	O
stochastic	B-Algorithm
scheduling	I-Algorithm
problems	O
can	O
be	O
regular	O
objectives	O
such	O
as	O
minimizing	O
the	O
total	O
flowtime	O
,	O
the	O
makespan	B-Algorithm
,	O
or	O
the	O
total	O
tardiness	O
cost	O
of	O
missing	O
the	O
due	O
dates	O
;	O
or	O
can	O
be	O
irregular	O
objectives	O
such	O
as	O
minimizing	O
both	O
earliness	O
and	O
tardiness	O
costs	O
of	O
completing	O
the	O
jobs	O
,	O
or	O
the	O
total	O
cost	O
of	O
scheduling	B-Application
tasks	O
under	O
likely	O
arrival	O
of	O
a	O
disastrous	O
event	O
such	O
as	O
a	O
severe	O
typhoon	O
.	O
</s>
<s>
The	O
performance	O
of	O
such	O
systems	O
,	O
as	O
evaluated	O
by	O
a	O
regular	O
performance	O
measure	O
or	O
an	O
irregular	O
performance	O
measure	O
,	O
can	O
be	O
significantly	O
affected	O
by	O
the	O
scheduling	B-Application
policy	O
adopted	O
to	O
prioritize	O
over	O
time	O
the	O
access	O
of	O
jobs	O
to	O
resources	O
.	O
</s>
<s>
The	O
goal	O
of	O
stochastic	B-Algorithm
scheduling	I-Algorithm
is	O
to	O
identify	O
scheduling	B-Application
policies	O
that	O
can	O
optimize	O
the	O
objective	O
.	O
</s>
<s>
The	O
Bayesian	O
method	O
has	O
been	O
applied	O
to	O
treat	O
stochastic	B-Algorithm
scheduling	I-Algorithm
problems	O
with	O
incomplete	O
information	O
.	O
</s>
<s>
Admissible	O
policies	O
must	O
be	O
nonanticipative	O
(	O
scheduling	B-Application
decisions	O
are	O
based	O
on	O
the	O
system	O
's	O
history	O
up	O
to	O
and	O
including	O
the	O
present	O
time	O
)	O
and	O
nonpreemptive	O
(	O
processing	O
of	O
a	O
job	O
must	O
proceed	O
uninterruptedly	O
to	O
completion	O
once	O
started	O
)	O
.	O
</s>
<s>
The	O
simplest	O
types	O
of	O
MQNs	O
involve	O
scheduling	B-Application
a	O
number	O
of	O
job	O
classes	O
in	O
a	O
single	O
server	O
.	O
</s>
<s>
The	O
majority	O
of	O
studies	O
on	O
stochastic	B-Algorithm
scheduling	I-Algorithm
models	O
have	O
largely	O
been	O
established	O
based	O
on	O
the	O
assumption	O
of	O
complete	O
information	O
,	O
in	O
the	O
sense	O
that	O
the	O
probability	O
distributions	O
of	O
the	O
random	O
variables	O
involved	O
,	O
such	O
as	O
the	O
processing	O
times	O
and	O
the	O
machine	O
up/downtimes	O
,	O
are	O
completely	O
specified	O
a	O
priori	O
.	O
</s>
<s>
Examples	O
of	O
scheduling	B-Application
with	O
incomplete	O
information	O
can	O
be	O
found	O
in	O
environmental	O
clean-up	O
,	O
project	O
management	O
,	O
petroleum	O
exploration	O
,	O
sensor	O
scheduling	B-Application
in	O
mobile	O
robots	O
,	O
and	O
cycle	O
time	O
modeling	O
,	O
among	O
many	O
others	O
.	O
</s>
<s>
When	O
the	O
scheduling	B-Application
policy	O
is	O
static	O
in	O
the	O
sense	O
that	O
it	O
does	O
not	O
change	O
over	O
time	O
,	O
optimal	O
sequences	O
are	O
identified	O
to	O
minimize	O
the	O
expected	O
discounted	O
reward	O
and	O
stochastically	O
minimize	O
the	O
number	O
of	O
tardy	O
jobs	O
under	O
a	O
common	O
exponential	O
due	O
date	O
.	O
</s>
<s>
When	O
the	O
scheduling	B-Application
policy	O
is	O
dynamic	O
in	O
the	O
sense	O
that	O
it	O
can	O
make	O
adjustments	O
during	O
the	O
process	O
based	O
on	O
up-to-date	O
information	O
,	O
posterior	O
Gittins	O
index	O
is	O
developed	O
to	O
find	O
the	O
optimal	O
policy	O
that	O
minimizes	O
the	O
expected	O
discounted	O
reward	O
in	O
the	O
class	O
of	O
dynamic	O
policies	O
.	O
</s>
