Revisiting correlations and scheduling in Web servers

Mathematical models play an important role in the design, analysis, control, optimization, management andplanning of Web server systems. To be most effective in each of these areas, such models must capture in sufficient detail the key characteristics of Web server workloads, the key characteristics of Web server scheduling policies for executing these workloads, and the impact of these workload and scheduling policy characteristics on Web server performance and related measures . Of particular interest in our study are very efficient mathematical methods that can be exploited online to support an increasingly important range of real-time applications (e .g., dynamic control of quality of service in Web servers to best satisfy service-level agreements), as well as in efficient interactive tools often used offline for many different purposes (e.g., what-ifanalysis and stochastic optimization for capacity planning). A significant body of research has investigated the workloads found in practice at a wide variety of Web server environments ; e.g . , see [1, 8, 18]. Most of these studies have demonstrated that the client request patterns exhibited at many different types of Web server environments have strong dependence structures and that the requested files sizes at these Web servers are independent and identically distributed (i .i .d.) according to a heavy-tailed or subexponential distribution . However, the vast majority of these studies appear to have completely ignored the issue of whether there is any correlation between the client request arrival times and the requested file sizes or the request service times. This includes studies of Web server workload characterization and generation, Web server performance models, and Web server scheduling policies . In this study, we consider data from various commercial Web server environments to revisit the issues of different forms of correlation in these Web server workloads and their implications on Web server performance and scheduling policies . Theresults ofour data analysis demonstrate the existence ofsignificant dependencies between the client request interarrival times and the corresponding file sizes and service times. Our analysis also shows a strong dependence structure within the interarrival process of client requests, whereas the sequence of service times is essentially i . i . d . To the best ofour knowledge, this is the first study to identify and quantify significant dependencies between the arrival and service processes in Web server environments (as opposed to network environments, where this issue goes all the way back to Kleinrock [15]). We then investigate the source of this cross correlation between the client request interarrival times and the corresponding file sizes and service times. The results of our data analysis support the view that such cross correlations are primarily due to certain mixing effects involving the superposition of different classes of client requests each with different service requirements . We next turn to consider a mathematical analysis of queueing Mark S. Squillante Mathematical Sciences Department IBM Thomas J. Watson Research Center Yorktown Heights, NY 10598, USA mss@watson . ibm . com