Queueing theory provides fundamental tools to study the performance of computer

and telecommunication networks. Basically, a model is developed, whereupon

performance measures are deduced by which the scenario at hand can be

evaluated. In a queueing model, broadly speaking, customers (packets, processes)

arrive and are stored in a buffer in awaitance of their service (transmission, being

executed). A popular and effective technique to obtain performance measures,

such as the average number of stored packets, makes use of so-called probability

generating functions. However, in a broad range of scenarios, the resulting formulas

for the performance measures contain various boundary probabilities that have

to be calculated numerically, which is a drawback for applicability. The purpose

of this project is to obtain accurate closed-form (i.e., no numerical calculations

required) approximations for the performance measures in such cases.