Retrial Queuing Models of Multi-Wavelength FDL Feedback Optical Buffers

Cataloged from PDF version of article.Optical buffers based on Fiber Delay Lines (FDL) have been proposed for contention resolution in optical packet/burst switching systems. In this article, we propose a retrial queuing model for FDL optical buffers in asynchronous optical switching nodes. In the considered system, the reservation model employed is of post-reservation type and optical packets are allowed to re-circulate over the FDLs in a probabilistic manner. We combine the MMPP-based overflow traffic models of the classical circuit switching literature and fixed-point iterations to devise an algorithmic procedure to accurately estimate blocking probabilities as a function of various buffer parameters in the system when packet arrivals are Poisson and packet lengths are exponentially distributed. The proposed algorithm is both accurate and fast, allowing one to use the procedure to dimension optical buffers in next-generation optical packet switching systems

System-theoretical algorithmic solution to waiting times in semi-Markov queues

Cataloged from PDF version of article.Markov renewal processes with matrix-exponential semi-Markov kernels provide a generic tool for modeling auto-correlated interarrival and service times in queueing systems. In this paper, we study the steady-state actual waiting time distribution in an infinite capacity single-server semi-Markov queue with the auto-correlation in interarrival and service times modeled by Markov renewal processes with matrix-exponential kernels. Our approach is based on the equivalence between the waiting time distribution of this semi-Markov queue and the output of a linear feedback interconnection system. The unknown parameters of the latter system need to be determined through the solution of a SDC (Spectral-Divide-and-Conquer) problem for which we propose to use the ordered Schur decomposition. This approach leads us to a completely matrix-analytical algorithm to calculate the steady-state waiting time which has a matrix-exponential distribution. Besides its unifying structure, the proposed algorithm is easy to implement and is computationally efficient and stable. We validate the effectiveness and the generality of the proposed approach through numerical examples. © 2009 Elsevier B.V. All rights reserve

TELPACK: An Advanced teletraffic analysis package

Performance evaluation of computer and communication networks gives rise to teletraffic problems of potentially large dimensionality. We briefly summarize a unifying system theoretic approach to efficient solution of a diversity of such problems, and introduce TELPACK, a publicly available software that implements this approach

Matrix-geometric solutions of M/G/1-type Markov chains: A unifying generalized state-space approach

In this paper, we present an algorithmic approach to find the stationary probability distribution of M/G/1-type Markov chains which arise frequently in performance analysis of computer and communication networ ks. The approach unifies finite- and infinite-level Markov chains of this type through a generalized state-space representation for the probability generating function of the stationary solution. When the underlying probability generating matrices are rational, the solution vector for level k, x k, is shown to be in the matrix-geometric form x k+1 = gF k H, k ≥ 0, for the infinite-level case, whereas it takes the modified form x k+1 = g 1F 1 kH 1 + g 2F 2 K-k-1 H 2, 0 ≤ k < K, for the finite-level case. The matrix parameters in the above two expressions can be obtained by decomposing the generalized system into forward and backward subsystems, or, equivalently, by finding bases for certain generalized invariant subspaces of a regular pencil λE - A. We note that the computation of such bases can efficiently be carried out using advanced numerical linear algebra techniques including matrix-sign function iterations with quadratic convergence rates or ordered generalized Schur decomposition. The simplicity of the matrix-geometric form of the solution allows one to obtain various performance measures of interest easily, e.g., overflow probabilities and the moments of the level distribution, which is a significant advantage over conventional recursive methods

Characterization of the Metabolic Phenotype of Rapamycin-Treated CD8+ T Cells with Augmented Ability to Generate Long-Lasting Memory Cells

Cellular metabolism plays a critical role in regulating T cell responses and the development of memory T cells with long-term protections. However, the metabolic phenotype of antigen-activated T cells that are responsible for the generation of long-lived memory cells has not been characterized.. than untreated control T cells. In contrast to that control T cells only increased glycolysis, rapamycin-treated T cells upregulated both glycolysis and oxidative phosphorylation (OXPHOS). These rapamycin-treated T cells had greater ability than control T cells to survive withdrawal of either glucose or growth factors. Inhibition of OXPHOS by oligomycin significantly reduced the ability of rapamycin-treated T cells to survive growth factor withdrawal. This effect of OXPHOS inhibition was accompanied with mitochondrial hyperpolarization and elevation of reactive oxygen species that are known to be toxic to cells.Our findings indicate that these rapamycin-treated T cells may represent a unique cell model for identifying nutrients and signals critical to regulating metabolism in both effector and memory T cells, and for the development of new methods to improve the efficacy of adoptive T cell cancer therapy

Infinite- and finite-buffer Markov fluid queues: A unified analysis

In this paper, we study Markov fluid queues where the net fluid rate to a single-buffer system varies with respect to the state of an underlying continuous-time Markov chain. We present a novel algorithmic approach to solve numerically for the steady-state solution of such queues. Using this approach, both infinite- and finite-buffer cases are studied. We show that the solution of the infinite-buffer case is reduced to the solution of a generalized spectral divide-and-conquer (SDC) problem applied on a certain matrix pencil. Moreover, this SDC problem does not require the individual computation of any eigenvalues and eigenvectors. Via the solution for the SDC problem, a matrix-exponential representation for the steady-state queue-length distribution is obtained. The finite-buffer case, on the other hand, requires a similar but different decomposition, the so-called additive decomposition (AD). Using the AD, we obtain a modified matrix-exponential representation for the steady-state queue-length distribution. The proposed approach for the finite-buffer case is shown not to have the numerical stability problems reported in the literature

Solving the single server semi-Markov queue with matrix exponential kernel matrices for interarrivals and services

Markov renewal processes with semi-Markov kernel matrices that have matrix-exponential representations form a superset of the well-known phase-type renewal process, Markovian arrival process, and the recently introduced rational arrival process. In this paper, we study the steady-state waiting time distribution in an infinite capacity single server queue with the auto-correlation in interarrival and service times modeled with this general Markov renewal process. Our method relies on the algebraic equivalence between this waiting time distribution and the output of a feedback control system certain parameters of which are to be determined through the solution of a well known numerical linear algebra problem, namely the SDC (Spectral-Divide-and- Conquer) problem. We provide an algorithmic solution to the SDC problem and in turn obtain a simple matrix exponential representation for the waiting time distribution using the ordered Schur decomposition that is known to have numerically stable and efficient implementations in various computing platforms. Copyright 2006 ACM