Overbooking's problem for a case of a random environment existence

Alexander Andronov, Diana Santalova
An overbooking policy assumes that a booking of some product or service exceeds given possibilities. It takes into consideration that a part of the booking will be cancelled. This situation is considered following to examples of aviation ticket booking. It is supposed that an external random environment exists. The environment is described as a continuous-time finite irreducible Markov chain. A demand on the booking depends on the state of the random environment. We consider such indices as the average number of engaged seats, the probability that passenger with bought or booked ticket encounters a refusal etc. A numerical example is considered.