Abstract:
In this paper, some tips and tricks for algebraic manipulations are utilized to
explicitly get the mean and variance of the duration of the busy period in a discretetime
finite-buffer vacation queue. Applying the law of total expectation, the closedform
expressions for the first two moments of the busy period initiated with an
arbitrary number of customers are firstly derived. Then, by employing the queue
length distri-bution at vacation termination and the quantities that mentioned above,
we give the stochastic decomposition structure of the busy period. Finally, in order to
ensure the reliability of the analytical approach, an effective way to validate the
correctness of our results along with a numerical example is also provided. We may
find that these simple tips and tricks can greatly reduce the difficulty of problem
solving.
