On Perfect Simulation of Markovian Queueing Networks with Blocking
Perfect simulation of a class of Markovian queueing networks with finite buffers is examined in this monograph. The network processes defined are modelled by restricted multivariate birth and death processes with intensities depending on a random environment. The random environments are mainly a set of independent onoff processes. Several simulation experiments illustrate the use of the perfect sampling algorithm and properties of the networks.
The class of networks is analysed by coupling techniques, and monotonic properties for network trajectories are established. The networks are simulated by embedding a coupling, which imposes an ordering of network trajectories, in a two-dimensional Poisson process, and by using a monotone Propp-Wilson algorithm. The effectiveness of the algorithm is examined by a series of simulation experiments and is found to be satisfactory. The defined networks can be extended to handle batch arrivals, rerouting of blocked units, buffer sizes varying over time, and other types of environments.
The class of networks devised can be used as a model for a wide range of applications in which the Markovian assumptions are satisfied. Even for complex and large networks, samples are obtained in a reasonable amount of time although the simulation time is hard to predict beforehand.
MSC 2000 subject classifications: 60K20, 60K25, 68M20, 90B22, 65C05, 60E15, 60J80
birth and death processes
Monte Carlo methods