On applications of computer algebra systems in queueing theory calculations

In the present paper, the most important aspects of computer algebra systems applications in complicated calculations for classical queueing theory models and their novel modifications are discussed. We mainly present huge computational possibilities of Mathematica environment and effective methods of obtaining symbolic results connected with the most important performance characteristics of queueing systems. First of all, we investigate effective solutions to computational problems appearing in queueing theory such as: finding final probabilities for Markov chains with a huge number of states, calculating derivatives of complicated rational functions of one or many variables with the use of classical and generalized L'Hospital's rules, obtaining exact formulae of Stieltjes convolutions, calculating chosen integral transforms used often in the above-mentioned theory and possible applications of generalized density function of random variables and vectors in these computations. Some exemplary calculations for practical models belonging both to classical models and their generalizations are attached as well.