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A general treatment of discrete-time buffers with one randomly interrupted output line

1986; Elsevier BV; Volume: 27; Issue: 1 Linguagem: Inglês

10.1016/s0377-2217(86)80008-x

1872-6860

Herwig Bruneel,

Real-Time Systems Scheduling

A discrete-time buffer with one single output channel, synchronous transmission of messages and an infinite waiting room is considered, where the output line is subjected to random interruptions in time. The stochastic nature of the interruption process is described by two independents sets of i.i.d. random variables: 'available periods', during which the output line is available for the transmission of data from the buffer, and 'blocked periods', during which it is not. It is shown how expressions of the probability generating function of the buffer occupancy at random clock times can be derived, under the assumption that both available and blocked periods are arbitrarily distributed with the restriction that the available periods have a rational probability generating function. Many prior treatments of this kind of buffer system are shown to be special cases of the present one. An illustrative example of the method is given.