# Analysis of the Macroscopic Behavior of Server Systems in the Internet Environment
## 2 Problem of Observing the Dynamics of Server Systems
In the actual operation and management of the server system, methods to determine the timing of scaling based on the utilization rate of computing resources are widely used. These are methods for monitoring the utilization rate of computing resources, such as CPU, memory, and storage allocated to virtual machines (VMs), and applying the scaling operation based on a preset resource utilization threshold [4; 5; 6]. In this method, because the scaling operation is performed when the utilization rate of the computing resources allocated to VMs increases, it is possible to prevent the service from being overloaded. When applying this method to an actual server system, it is necessary to consider the overhead that accompanies capturing the state of the service, and researchers have highlighted that it is difficult to accurately measure the utilization rate of a computing resource in a virtual environment [7]. Additionally, research on a scaling method that considers QoS, which is an index of the operational status and performance of services provided by the system, has been proposed [8; 9; 10]. Considering the actual state of services, it is possible to incorporate specific operational targets, such as a service level agreement (SLA) and service level objective (SLO), as a guide for scaling. In commercial systems, QoS-based approaches are adopted that solve optimization problems to maximize QoS while minimizing operational costs according to policy of each service provider [11; 12; 13]. Operational costs include QoS violation penalties, power consumption and time to migrate/replicate VMs as well as pricing of computing resources. Although scaling policy varies depending on the organization, it is essential in common that administrators accurately capture QoS as they can and the operational status of server systems changing dynamically. When scaling is executed based on the observation of the QoS, it is necessary to capture the relation between the amount of computing resources allocated to VMs and QoS, that is, the operational characteristics of the server system, in advance. Existing scaling methods have highlighted practical issues, such as restricting elasticity, which is an advantage of the cloud environment in terms of requiring prior knowledge or the offline profiling of specific services [8]. QoS is widely used in various systems as a means to capture the status of running systems. By contrast, in the actual operation of a server system, it is empirically known that the system has nonlinear dynamics and its QoS degrades catastrophically under overloaded conditions, and this has also been confirmed in experiments concerning the performance management of a server system [2; 3; 14; 15; 16]. To summarize, QoS decline occurs because of the property that it can only be observed after an event, such as overload or resource depletion, has already occurred. Therefore, it cannot be detected beforehand that the server system falls into an undesirable state only by observing the QoS. Various benchmark tools, such as httperf [17], S-Client [18], JMeter [19], and Tsung [20], have been proposed and used to measure the operational characteristics of a server system. Using these benchmark tools, administrators can capture the operational characteristics of the server system, that is, the relation between the load on the server system and its QoS. Based on an analysis of the operational characteristics obtained using benchmark tools, it is possible to estimate the performance limit and maximum permissible load of the server system, and to apply the results of the analysis to the actual control of the server system. Furthermore, many studies have been conducted on analytical models to theoretically consider the dynamics of a server system [21; 22; 23; 24]. These studies have attempted to model the behavior of the server system based on queuing theory or other approaches to analyze and infer the operational characteristics of the server system.