Long range dependence in cloud servers: a statistical analysis based on Google workload trace

Analysis and characterization of cloud workloads provides crucial information for designing optimal resource management policies. In this work, we propose to analyse long range dependence nature of cloud resource workloads. Long range dependence is a phenomenon widely studied in Ethernet and Internet traffic. But there is a dearth of works that analyse long range dependence in cloud workloads. In this work, we propose to verify the presence of long range dependence in cloud workloads using autocorrelation analysis and rescaled range analysis method. In addition to experimental evidence, studies on long range dependence are incomplete without a sound theoretical justification in support of its origins in cloud workloads. In this context, we propose to analytically analyse, aggregate workload in the datacenter using different metrics like arrival, service distributions of jobs and their resource usage. For a dependable explanation of long range dependence in cloud workloads, we analyse workloads from standard real dataset of Google cluster trace. Based on the analysis, we see that analysed metrics display heavy tailed behaviour and using a mathematical formulation, we prove that aggregate workload exhibits long range dependence.