Ph.D Thesis

Ph.D StudentNossenson Ronit
SubjectStochastic Models for Web Servers
DepartmentDepartment of Computer Science
Supervisor PROF. Hagit Attiya


A stochastic server system is characterized by the client arrivals process and by the service-time distribution. Considering Web servers, the client requests are interpreted as file requests and the service-times are interpreted as the files' transmission-durations. It is known that the arrival process of Web servers is an ON/OFF process, with heavy-tailed ON times, OFF times and inter-arrival times within the ON-times distributions. Moreover, the files' transmission-duration distribution was shown to be heavy-tailed as well. Such distributions are characterized by extremely high variability, and create self-similar behavior.

Here we present a detailed description of the arrivals and service of Web servers. Using simulation and Web trace analysis, we investigate both the influence of each arrival parameter on the system performance and the reasons for the heavy-tailed behavior of the transmission duration. Next, the accuracy of self-similar processes that are used to model Web servers is evaluated using simulations. We present evidence that when the system has low to medium utilization, processes with either realistic arrivals or realistic service, but not both, do not estimate the performance parameters in a reliable manner.

Finally, we introduce two models for Web servers that consider both realistic arrivals and realistic service. First, a simple Markovian model, called the N-Burst/ME/1 model.  Its queue-length distribution, waiting-time distribution, and buffer-overflow probability are given. Second,  a more complicated and accurate model called the N-Burst/G/1 model with heavy-tailed service-time distribution. An asymptotic calculation of its waiting-time distribution is presented; this relies on calculating the waiting-time distribution in the M/G/1 model with heavy-tailed service-time distribution.