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Some martingales in dams with Poisson input and release. (English) Zbl 0545.60092
We consider two dams. The first one is the infinite dam in which inputs form an additive process and outputs form a compound Poisson process with exponential jumps. The second one is the finite dam in which both inputs and outputs form compound Poisson processes with exponential jumps. For these models we obtain the Laplace-Stieltjes transforms of the time to the first emptiness and of the time to the first overflow, respectively. We apply the method using martingale properties described by D. P. Kennedy, Stochastic processes, Appl. 4, 261-269 (1976; Zbl 0338.60030).
60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)