A computational approach for a fluid queue driven by a truncated birth-death process

In this paper, we consider a fluid queue driven by a truncated birth-death process with general birth and death rates. We find the equilibrium distribution of the content of the fluid buffer by computing the eigenvalues and eigenvectors of an associated real tridiagonal matrix. We provide efficient procedures which avoid numerical instability, to a greater extent, arising in a straightforward calculation of these quantities by standard procedures. In particular, we reduce the order of the matrix by one and show that this reduced matrix can be made symmetric and hence we could make use of the stable and efficient method of bisection to compute the eigenvalues. The effectiveness of these procedures is illustrated through tables and graphs. \u

Exact transient analysis of a circulant queuing network

AbstractCirculant matrices possess unusual and interesting properties. These properties have been exploited to obtain the transient solution in closed form for a circulant queuing network that models a distributed query processing system. The sojourn time of a customer in the circulant queuing network is determined. A semi-Markov generalisation of this network is also studied

Fluid queues driven by an M/M/1/N queue

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 specific cases, we verify the results available in the literature

A birth-death process suggested by a chain sequence

We consider a birth-death process whose birth and death rates are suggested by a chain sequence. We use an elegant transformation to find the transition probabilities in a simple closed form. We also find an explicit expression for time-dependent mean. We find parallel results in discrete time. Finally, we show that the processes under investigation are transient, and hence, the stationary distribution does not exist