572 Large Scale and Big Data
and cold, respectively) can accept a job is computed by VM provisioning sub-
models. The RPDE submodel uses these probabilities as input parameters. Output
measures such as rejection probability due to buffer full (P
block
), rejection prob-
ability due to insufcient capacity (P
drop
), and their sum (P
reject
) are obtained from
the RPDE submodel. Observe that P
block
computed in the RPDE submodel is used
as an input parameter in VM provisioning submodels. Also, outputs from VM
provisioning submodels (P
h
, P
w
, P
c
) are needed as input parameters to solve the
RPDE submodel. Hence, there is a cyclic dependency among the submodels. Such
dependency is resolved using xed-point iteration [14,17]. Proof of existence of a
sol