Scalable Stochastic Model for IaaS Cloud Computing

A STUDY REPORT OF SCALABLE STOCHASTIC MODEL 

Introduction

                Today, cloud computing becomes more popular among users, and the market of the large cloud computing services is intensely competitive among large IaaS (Infrastructure as a Service) cloud providers such as Amazon AWS, Google. Cloud provided service’s performance is a decisive factor for the service contract. There are three choices for a cloud performance evaluation: (1) performance analysis based on discrete event simulation, (2) performance analysis based on experiment, and (3) performance analysis based on the stochastic model. The first two choices are inefficient in time and cost due to a large number of computer resources used in simulation and experiment (Duke University, 2013). The third choice, i.e., the stochastic model appears a low-cost option with time-effectiveness. However, the stochastic model has scalability problem due to the large size and complexity of a cloud system, particularly a high growth of the model states and system components (Sakr & Gaber, 2014). This Unit 3 Individual Project’s document will describe the main concept of the stochastic model, address the proposed stochastic model based on three-pool cloud architecture, its limitation, and solutions, then discuss the potential applications of this stochastic model.

Main Concept

               To improve the performance of the large IaaS cloud computation and services on hardware, software, workload and management characteristics, Sakr and Gaber (2014) proposed a simpler and scalable stochastic model from Markov’s large stochastic model that tends to have many modeling states and a lot of system components. Sakr and Gaber’s simplified stochastic model focuses on lower cost due to fewer computer resources, and less response time delays due to no simulation or experiment. It has two primary features, i.e., scalability and tractability, and uses a three-pool cloud architecture that includes some interacting sub-models such as RPDE (Resource Provisioning Decision Engine) sub-model, pool sub-models, and VM provisioning sub-models as shown in Figure 1 below.

Figure 1: Interactions among the sub-models

Source: Adapted from Sakr and Gaber, 2014.

The simplified stochastic model offers a unique closed-form solution with stochastic modeling software packages, e.g., SHARPE or SPNP by using fixed-point iteration (Ghosh, Longo, Naik & Trivedi. 2012; Hirel, Tuffin & Trivedi, 2000; Trivedi & Sahner, 2009).

Scalable three-pool cloud architecture

Since processing large-scale data IaaS cloud computing is complex, Markov’s stochastic architectural model that use a large-size hardware and sophisticated software. It is difficult to scale up and scale out the Markov’s system. Sakr and Gaber’s simplified stochastic model uses three-pool cloud architecture with scalability feature. In the three-pool cloud architecture, physical machines (PMs) such as computer resources are grouped into three hot, warm and code pools that depend on power consumption and response time. The hot pool includes the PMs that are on and in a ready state where VMs (virtual machines) wait for configuration for user request with maximum power consumption and the least response time. The warm pool consists of PMs in sleep mode that waits for next run. And the cold pool is PMs that are in Off state with minimum power and the longest elapsed response time (Ghosh, Naik & Trivedi, 2011). The RPDE tries to find an available PM in the hot, warm, or cold pool respectively to accept the service request as shown in Figure 2 below. Service request rejection probability and provisioning response delay are two elements in performance analysis metrics.        

Figure 2: A three-pool cloud architecture with a service request for a PM.

Source: Adapted from Sakr and Gaber, 2014.

The simplified stochastic three-pool cloud architecture-based model has a key advantage of scalability. It has a set of independent sub-models, and each sub-model can represent each PM in the pool. Some VMs running on a PM is kept track by those sub-models. The interactions among sub-models promote the overall model to become scalable and tractable. The characteristic of interacting sub-models makes the simplified stochastic system easily scale out by adding the new computer(s). Non-zero entries and reduction of some states allow solution time to be reduced significantly. As a result, users use this scalable and tractable stochastic model to detect performance bottlenecks, do what-if analysis, or plan capacity of the system (Sakr & Gaber, 2014). For example, overall mean response delay time, mean queuing delay, or bottleneck component shifts since the mean service time and PMs in the pool are changed. Furthermore, grouping the PMs or computer resources into multiple pools allow the provider monitors power consumption and response time to adjust service offering to clients and users.

Limitation of the three-pool cloud architecture

            The main limitation of the three-pool cloud architecture model is that the service request may be rejected. The service request rejection can occur when the entrant buffer is full, or the resource provisioning decision engine cannot find an available PM due to insufficient capacity. In most of the cases, all PMs in the hot, warm or cold pool are not available with increasing response delay time significantly. To remove this limitation, Sakr and Gaber (2014) use Markov approach of the expected steady-state reward rate for the probability of the service request (Trivedi, 2001). Sakr and Gaber’s analysis shows that the longer mean service time is, the higher service request rejection probability is. With increasing the PM capacity, service request rejection probability is decreased.

Another limitation of the three-pool cloud architecture model is the service requests’ characteristic. Service requests must be homogeneous, and PMs are also homogeneous. They should be alike, identical or the same type. Also, each service request is required for one unique VM instance with specific RAM, CPU, and disk capacity. Otherwise, the simplified three-pool cloud architecture model will not work properly. Notice that VM provisioning sub-models can be extended to heterogeneous PMs. These heterogeneous PMs can be categorized into multiple classes, and each class can be represented by a pool such that PMs can be homogeneous within a pool but heterogeneous across the pools.

Potential applications

            Using SHARPE Portal (Symbolic Hierarchical Automated Reliability and Performance Evaluator), users can compute (1) service request rejection probability and (2) mean response delay time for solving the interacting sub-models (Duke University, 2017). The service request rejection probability is proportional to the mean service time. The simplified stochastic model can be used to perform what-if analysis for the entire system. In the mean response delay, bottlenecks may shift while the mean service time and cloud capacity or PMs in each pool are varied. The accuracy and scalability of the simplified stochastic model can be computed in a variant of stochastic Petri net such as SRN (stochastic reward net) (Hirel, Tuffin & Trivedi, 2000). Stochastic Petri Net Package (SPNP) can be used to solve the monolithic SRN model. The reduced number of states and nonzero entries in the interacting sub-models promotes a decrease in solution time.

Scalability of the simplified stochastic model can be applied on modeling the large IaaS pools in Big Data processing environments. Notice that the model in the analysis uses three-pools. The approach can be expanded more than three pools. One CTMC (Continuous Time Markov Chain) is needed for a VM provisioning sub-model for each pool. The simplified stochastic model can scale linearly with numbers of pools in the cloud. As addressed previously, the homogeneous PMs can be expanded to heterogeneous PMs categorized into different classes such that PMs are homogeneous within a pool but heterogeneous across the pools. The VM provisioning sub-models can be expanded into parallel provisioning of the service requests. Based on the simplified stochastic model, new software packages and analytical tools can be developed for Big Data applications.

Conclusion

In three choices for a cloud performance evaluation, the last choice of the simplified, scalable stochastic model was one of the most favorite solutions in effective cost and time-effectiveness. The main concept of the simplified stochastic model proposed by Sakr and Gaber (2014) was discussed thoroughly. The simplified stochastic model’s scalability and practice were discussed in performance analysis on IaaS cloud computing environment. The document also discussed the main limitations and provided some techniques to remove the limitations. Also, the potential applications of the simplified stochastic model are provided in depth to the audience for future research.

REFERENCES

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