# Analysis of the Macroscopic Behavior of Server Systems in the Internet Environment
## 2 Problem of Observing the Dynamics of Server Systems  
When operating a server system that utilizes the elasticity of the cloud environment, to maintain the service stably, it is important to scale the service by controlling the amount of computing resources given to the server system according to fluctuating user demand. The demand of the service user and the amount of computing resources given to the server system is in a trade-off relation, as shown in Figure 1. In the scenario of under-provisioning, in which the amount of computing resources is insufficient for service demand, the service becomes overloaded. By contrast, the scenario of over-provisioning, in which the amount of computing resources becomes excessive, is undesirable from the viewpoint of cost and power consumption because computing resources allocated to the service are wasted. The administrator must recognize the operational state of the service and execute scaling at the right time; however, it is difficult to properly capture the timing. This is because the operational characteristics of the server system change irregularly according to the fluctuating operational state of the service. Figure 1: Resource management of cloud-hosted services. Figure 2 shows the relation between the degree of activity of the server system (\(x\)) and amount of processing data (\(\mu\)), that is, the system characteristic called throughput (\(T\)), which represents the processing capabilities of the server system. Theoretically, this graph has a monotonically increasing and saturated shape like \(T_{ideal}\). However, in actual operation, this demonstrates dome-shaped characteristics like \(T_{real}\). In the overloaded state, in which throughput exceeds the limit state at which throughput is maximized, throughput degrades even if the degree of activity of the server system increases. Generally, it is not easy to specify where the state of the running server system is on \(T_{real}\). For example, it is impossible to assess that the system operating near state \(a\) is approaching the limit state \(m\), or that the system is now operating in overloaded state \(b\) and exceeding limit state \(m\). Therefore, prior to the operation of the server system, the throughput characteristic in a predetermined scenario is captured using model analysis, and at the time of actual system operation, the system operating state is estimated using the characteristic and measured values of \(x\) and \(\mu\). Then, for example, when it is assumed that the system is shifting from state \(a\) to state \(m\), to maintain the degree of activity of the system, the amount of processing data is adjusted or the scaling operation is performed. Although the function or configuration of the system changes because of such a scaling operation, the throughput characteristics also change, as shown in Figure 3. If the scaling operation changes the throughput characteristics from \(T(t_{0})\) to \(T(t_{1})\), the system performance limit also changes from state \(m\) to state \(b\). However, in the case in which the changed characteristic \(T(t_{1})\) is unidentified, it becomes very difficult to recognize the operational state of the server system, which also hinders the operation of the system. For example, if it cannot be recognized that the system is in the state that exceeds the limit state \(x_{2}\), the system falls into an undesirable state. Figure 3: Change in throughput characteristics using the scaling operation. Figure 2: Throughput characteristics of the server system. To make full use of the elasticity of the cloud-hosted service that has the characteristics mentioned above, there have been various efforts related to system operation and control. One problem common to these methods is providing an effective method for precisely observing and capturing the system operational status that changes constantly according to irregularly incoming service requests.