Functions provided by Web applications are increasingly diverse which make their structures complicated and meshed. Cloud computing platforms provide elastic computing capacities for these meshed Web systems to guarantee Service Level Agreement (SLA). Though workloads of meshed Web systems usually change steadily and periodically in total, sometimes there are sudden fluctuations. In this paper, a hybrid State-space-model-and-Queuing-network based Feedback control method (SQF) is developed for auto-scaling Virtual Machines (VMs) allocated to each tier of meshed Web systems. For the case with workloads changing steadily, a State-space-model based static Feedback Control method (SFC) is proposed in SQF to stabilize request response times near the reference time. For unsteadily changing workloads, a Queuing-network based multi-tier collaborative Feedback Control method (QFC) is proposed for effectively eliminating bottlenecks. QFC builds a control system for each tier individually and uses the queuing network to measure the interaction relationships among different tiers. Experimental results show that QFC is able to improve the efficiency of eliminating bottlenecks (decreasing upper-limit SLA violation ratios by 31.99%$\sim$56.52%) with similar or a little bit high VM rental costs compared to existing methods while SFC obtains more stable response times for requests with reasonable additional costs.

Most of existing resource provisioning methods are designed for traditional Web applications with linear structures. However, Web systems with the meshed topology are becoming widespread. Meshed connections among different tiers make Virtual Machine (VM) provisioning and bottleneck elimination complex. In this paper, a Jackson network based Proactive and Reactive VM auto-scaling Method (JPRM) is proposed. In JPRM, request transition behaviors among tiers are modeled as a finite-state Markov stochastic process. A transition probability matrix is studied on-line to predict resource requirements based on M/M/N queuing models as proactive control. For reactive provisioning, the final increased request rate of each tier is determined based on stable state checking and Jackson equilibrium equation solving to eliminate bottleneck tiers and avoid bottleneck shifting. The JPRM is evaluated in a simulation environment established using CloudSim. Experimental results show that JPRM avoids bottleneck shifting with reasonable additional VM rental costs compared with existing methods.