Development of a methodology to increase the applicability of queueing models whereby numerical calculation of boundary probabilities is required

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.