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Z. Saffer:
"Optimization of Cloud Model Based on Shifted N-policy M/M/m/K Queue";
Talk: DataSys 2021 Congress, Spanien, online; 2021-05-30 - 2021-06-03; in: "AICT2021 The Seventeenth Advanced International Conference on Telecommunications", IARIA, (2021), ISBN: 978-1-61208-860-0; 11 - 20.

Abstract-In this paper, we present the performance analysis
and cost optimization of an Infrastructure-as-a-Service (IaaS)
cloud model with a capacity control policy. The Virtual Machines
(VM) are modeled 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 VMs. We define
a cost model, that the cloud provider encounters. It 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 VMs 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 VMs. We call it as shifted Npolicy. We provide the stationary analysis of the model. We
derive closed form results for the distribution of the number of
requests and 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 reduce the problem to a nonlinear equation
with a specific structure including factorial terms. We provide
the approximate solution of the optimization task. The major
result of the work is the closed form approximate solution
formula, which gives the optimal threshold under the most
relevant range of parameters. The formula gives insight into the
dependency of the optimum on the model and cost parameters.
We provide also illustrating examples for the most important
approximations and validate the approximate solution formula
by numeric optimization.

optimization; cloud model; queueing model; N-policy