Some Related Queueing Models with Dependent Service and Inter-Arrival Times.

摘要

Some related queueing models which allow for a type of dependence between service and inter-arrival times are discussed. Particular cases of the general models are the transition models, for which arrivals are generated by transitions in a Markov chain in continuous time. Possible applications for these models are production lines, doctor's appointments and storage situations. The stationary behavior of the forward and backward models is analyzed. The case of the forward model has been examined before, and quite general results are possible. The author considers how these results relate to the forward transition model. A complete analysis of the stationary behavior for backward models is achieved only in particular case of expotential arrivals, it is shown how to compute the Laplace transform of the stationary distribution of total waiting times. The authors also analyze the busy period distribution for the last model, and show how to compute the busy period transform. (Modified author abstract)