Businesses rely increasingly on Internet services as the basis of their income. Downtime and poor performance of such services can therefore be directly translated into loss of revenue. In order to plan and design services sufficiently capable of meeting minimumQuality of Service (QoS) requirements and Service Level Agreements(SLA), an understanding of how network traffic and job service demand affect the system is necessary. Traditionally, arrival and service processes have been modelled as Poisson processes. However, research done over the years suggests that the assumption of Poisson traffic is fallible in many cases. This work considers performance of a web server under different traffic and service demand conditions. Moreover, we consider theoretical models of queues, response time formulas derived from this models and their validity for a web server system. We try to make a simple approach to a complex problem by modelling a web server as one simple queueing system. In addition, we investigate the phenomenon known as self-similarity which has been observed in web traffic inter-arrival processes. We have found indications that traffic with identical expectation values for inter-arrival and service time differing in distribution type affects the response time differently. Moreover, classical queueingmodels are found unsuited for doing capacity planning. Instead we suggest ”a worst case scenario” approach in order for service providers to meet service level targets. Much of the previous work within these areas is of a highly mathematical and theoretical nature. We investigate from a more pragmatic viewpoint.