Fluid Queues Driven by an M/M/1/N Queue

R. B. LENIN ； P. R. PARTHASARATHY

《Mathematical Problems in Engineering》 2000卷 (2000/12) Pp. 439-460

https://doi.org/10.1155/S1024123X00001423

摘要

In this paper we consider fluid queue models with infinite buffer capacity which receives and releases fluid at variable rates in such a way that the net input rate of fluid into the buffer (which is negative when fluid is flowing out of the buffer) is uniquely determined by the number of customers in an M/M/1/N queue model (that is, the fluid queue is driven by this Markovian queue) with constant arrival and service rates. We use some interesting identities of tridiagonal determinants to find analytically the eigenvalues of the underlying tridiagonal matrix and hence the distribution function of the buffer occupancy. For specificcases, we verify the results available in the literature.

關鍵字

Tridiagonal matrices ； Tridiagonal determinants ； Eigenvalues ； Eigenvectors