Elements of the theory of dams

W ostatnich trzydziestu latach teoria tam (ang. theory of dams) rozwija się szybko i odczuwalny jest niedosyt dostępnych prac przeglądowych. Znakomite prace przeglądowe i monografie Morana [52], Prabhu [62], [63], Takacsa [83] i Ganiego [24] nie zawierają najnowszych kierunków badań. Praca ta ma na celu wypełnienie tej luki.

This paper is a review of recent results in theory of dams. Only continuous-time models are considered, the dam capacity being assumed to be infinite. The results are given for the following cases: (1) The input is a process with independent increments, and release is at a constant rate; (2) the input and output processes have infinitely divisible distributions; (3) the input is a process with independent increments, and the release rate is equal to r(x), where x denotes the content of the dam; (4) the input is a semi-Markov process, and the output rate is r(x); (5) the input and output are semi-Markov processes. The bibliography includes 88 items.