A Multiserver Approximation for Cloud Scaling Analysis

Queueing models of web service systems run at increasingly large scales, with large customer populations and with multiservers introduced by scaling up the services. "Scalable" multiserver approximations, in the sense that they that are insensitive to customer population size, are essential for solution in a reasonable time. A thorough analysis of the potential errors, which is needed before the approximations can be used with confidence, is the goal of this work. Three scalable approximations are evaluated: an equivalent single server SS, an approximation RF introduced by Rolia, and one based on a binomial distribution for queue state AB. AB and SS are suggested by previous work but have not been evaluated before. For AB and SS, multiple classes are merged into one to calculate the waiting. The analysis employs a novel traffic intensity measure for closed multiserver workloads. The vast majority of errors are less than 1%, with the worst cases being up to about 30%. The largest errors occur near the knee of the throughput/response time curves. Of the approximations, AB is consistently the most accurate and SS the least accurate.