Q-MAM: a tool for solving infinite queues using matrix-analytic methods

In this paper we propose a novel MATLAB tool, called Q-MAM, to compute queue length, waiting time and sojourn time distributions of various discrete and continuous time queuing systems with an underlying structured Markov chain/process. The underlying paradigms include M/G/1and GI/M/1-type, quasi-birth-death and non-skip-free Markov chains (implemented by the SMCSolver tool), as well as Markov processes with a matrix exponential distribution. We consider various single server queueing systems with phase-type, matrix exponential, Markovian, rational and semi-Markovian arrival and service processes; queues with multiple customer types, where the service depends on the customer type and where consecutive customer types may be correlated; and queues with multiple servers for which the typical dimensionality problem can be avoided. Apart from implementing various classical and more advanced solution techniques, the tool also extends and improves some of the existing solution techniques in a number of cases.