R.B. Lenin

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.

An inverse problem in birth and death processes

An inverse problem of constructing birth and death processes X(t)⊮n finite state space 0, 1, 2, …, N n0 ⊮s considered. Given a set of 2N + 1, distinct, nonnegative real numbers one of which is zero, say n0 = s0 < z1 < 2< … < zN < sN, n n na procedure is established to obtain the birth and death rates of a birth and death process so that nP(X(t)=0)=∑j=0NΠi=1N(zi −sjΠi=0,iǂjN(si − sje−sjt n n nother transient system size probabilities. This technique is illustrated numerically.

Fluid queues driven by a birth and death process with alternating flow rates

Fluid queue driven by a birth and death process (BDP) with only none negative effective input rate has been considered in the nliterature. As an alternative, here we consider a fluid queue in nwhich the input is characterized by a BDP with alternating npositive and negative flow rates on a finite state space. Also, nthe BDP has two alternating arrival rates and two alternating nservice rates. Explicit expression for the distribution function nof the buffer occupancy is obtained. The case where the state nspace is infinite is also discussed. Graphs are presented to nvisualize the buffer content distribution.

On The Numerical Solution Of Transient Probabilities Of Quadratic Birth And Death Processes

The transient system size probabilities for birth and death processes with quadratic birth and death rates are obtained by writing the Laplace transform of these probabilities as a continued fraction and finding the inversion through the properties of tridiagonal matrices. The effectiveness of this procedure is illustrated through tables and graphs, for an infinite capacity as well as for a finite capacity birth and death processes.