This report is a theoretical approach, using queuing systems, to describe delay characteristics of wireless telecommunication systems. In the report we derive the waiting time and total time distributions for two classes of queuing systems, namely G/M/1 and M/G/1.We give examples of particular queues belonging to each of these classes and analyse them. We find that the distributions are independent of packet size if the queuing discipline is first come first served, and that the total time distribution of the G/M/1 system is exponentially distributed regardless of the inter arrival process. We also apply the theories to a wireless radio system, HS-DSCH, and compare the theoretical results to simulation results. The M/E2/1 queue (with a constant delay added) is shown to be a good model of HS-DSCH. It also contains an example of how to use the calculated distributions to, given a certain delay tolerance, predict the behaviour of a new service in an existing system. The intended reader of this thesis is assumed to have some background in stochastic processes.