Transient analysis of a fluid queue driven by a birth and death process suggested by a chain sequence

摘要

We analyse the transient behaviour of a fluid queue driven by abirth and death process (BDP) whose birth and death rates aresuggested by a chain sequence. For the BDP suggested by a chainsequence, the stationary probabilities do not exist andhence the stationary buffer content distribution for fluid queues driven by such BDP does not exist.However, their transient distribution is obtained in a simpleclosed form by two different approaches: the first isthe continued fraction approach and the second is an approachin terms of recurrence relation by an analysis similarto that of Sericola (1998). The probability for thebuffer content to be empty at an arbitrary time is also studied.The variations in this performance measure are revealed in theform of graphs. Numerical illustrations are included.