Using the discrete time modelling approach to evaluate the time-dependent behaviour of queueing systems

Many real-life queueing problems exhibit time-dependent behaviour, but the corresponding theoretical models are hard to handle. The overall purpose of this paper is to describe a discrete time modelling (DTM) approach to solving problems of this sort, and to outline the research opportunities and challenges associated with it. The DTM approach is placed alongside other related research and is shown in particular to have strong links with some aspects of the matrix-geometric methods. The main research issues that have arisen in applying the DTM approach to problems of the form M(t)/G/1, M(t)/G/c and M(t)/G^0.c/1 are discribed. This then provides a basis for outlining ongoing research into systems such as M(t)/G/c/K and tandem queues. Finally DTM research opportunities and challenges for more complex problems such as priority queues, server vacation models and queueing networks are delineated.