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

Abstract

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

On the exact transient solution of fluid queue driven by a birth death process with specific rational rates and absorption

“…Parthasarathy, Sericola and Vijayashree [3] have considered a fluid queue model governed by a birth death process with state space {0, 1, . .…”

“…Thus substituting β = 1 4 in Theorem 5.1 of [3] the following solution is obtained. which coincides with our results given by Eqs.…”

“…Sericola and Guillemin [7] gave the transient solution for fluid queues driven by birth death process using continued fraction and recursive relations. Parthasarathy, Sericola and Vijayashree [3] found the transient solution for buffer distribution for fluid queues driven by birth death process suggested by a chain sequence using the similar approach of recursive polynomials. The same authors also found the transient solution for fluid queues modulated by an M/M/1 queue using recursive polynomials [4].…”

“…In this paper we assign rational birth and death rates to the background birth death process which form a chain sequence and use the methodology of continued fraction to find the buffer content distribution. The same methodology has been used by [3] to solve chain sequences, but this paper introduces the concept of absorption. We show how the solution is affected when μ 0 = 0, a common assumption in various other papers.…”

Cola de un fluido modulada por un proceso de Markov con finitos estados

“…They find analytically the eigen values of the underlying diagonal matrix and hence the steady state distribution function of the buffer occupancy. [8] and [5] presented the transient solution using a direct approach with the help of recurrence relations. In [8] the transient behavior of stochastic fluid flow models in which the input and output rates are controlled by a finite homogeneous Markov process is analyzed.…”