We obtain a single formula which, when its components are adequately chosen, transforms itself into the main formulas of the Palm theory of point processes: Little's L = λW formula [10], Brumelle's H = λG formula [5], Neveu's exchange formula [14], Palm inversion formula and Miyazawa's rate conservation law [12]. It also contains various extensions of the above formulas and some new ones.

This article reviews results related to event and time averages (EATA) for point process models, including PASTA, ASTA and ANTIPASTA under general hypotheses. In particular, the results for the stationary case relating the Palm and martingale approach are reviewed. The non-stationary case is discussed in the martingale framework where minimal conditions for ASTA generalizing earlier work are presented in a unified framework for the discrete- and continuous-time cases. In addition, necessary and sufficient conditions for ASTA to hold in the stationary case are discussed in the case even when stochastic intensities may not exist and a short proof of the ANTIPASTA results known to date are given.

This paper is a survey of the solutions of various first-passage time problems in the theory of queues.

It has been demonstrated by Takács in a series of papers and in his book that combinatorial methods can be successfully applied to derive certain probability distributions in queueing processes. In this paper, we further illustrate the usefulness of combinatorial techniques and determine the stochastic law of the busy period in two queueing systems particularly involving batches. It may be of interest to note that queues involving batches have been dealt with in [3] and [7].