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

Transient solution of a multiserver Poisson queue with N-policy

AbstractWe consider an M/M/c queueing system, where the server idles until a fixed number N of customers accumulates in a queue and following the arrival of the N-th customer, the server serves exhaustively the queue. We obtain the exact transient solution for the state probabilities of this N-policy queue by a direct approach. Further we obtain the time-dependent mean, variance of this system and its busy period distribution

A birth-death process suggested by a chain sequence

AbstractWe 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