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Z. Saffer:
"Cloud Cost Optimization Based on Shifted N-policy M/M/M/K Queue Model";
International Journal on Advances in Telecommunications, 14 (1&2) (2021), S. 70 - 99.

Cloud cost optimization is an important issue having
also impact on the economy of the Cloud service, since it
enables the Cloud service provider the service provisioning at
minimum cost. This paper provides the performance analysis
and cost optimization of an Infrastructure-as-a-Service Cloud
model with a capacity control policy. The Virtual Machines are
modelled as parallel resources, which can be either in active
or in standby state. The capacity of the cloud is controlled
by changing the number of active Virtual Machines. The cost
model, which the cloud provider encounters, takes into account
both energy consumption and performance measures. The major
objective of the work is to provide a tractable analytic model,
which is suitable for practical use. For this purpose, we model
the Cloud services by an M/M/M/K queue. We propose a
simple control policy, in which a predefined portion of Virtual
Machines are always active. The remaining ones are activated
simultaneously when the number of requests reaches a threshold
and deactivated when the number of requests falls below the
predefined portion of active Virtual Machines. We call this policy
as shifted N-policy. We provide the stationary analysis of the
model and derive closed form results for the distribution of the
number of requests as well as for several performance measures.
The cost model leads to a discrete optimization task, which
we approximate by a nonlinear continuous optimization task.
After applying numerous approximations, we provide, in form
of solution formulas, approximate solutions of the optimization
task in the two most relevant traffic ranges. We give illustrating
examples for the most important approximations and properties
of the model as well as validate the approximate solution formulas
by numeric optimization. The major results of the work are
the closed form approximate solution formulas, which give the
optimal threshold under the most relevant ranges of parameters
and provide insight into the dependency of the optimum on the
model and cost parameters.

optimization; cloud model; queueing model; Npolicy