Solving the ME/ME/1 queue with state-space methods and the matrix sign function

Cataloged from PDF version of article.Matrix exponential (ME) distributions not only include the well-known class of phase-type distributions but also can be used to approximate more general distributions (e.g., deterministic, heavy-tailed, etc.). In this paper, a novel mathematical framework and a numerical algorithm are proposed to calculate the matrix exponential representation for the steady-state waiting time in an ME/ME/1 queue. Using state–space algebra, the waiting time calculation problem is shown to reduce to finding the solution of an ordinary differential equation in state–space form with order being the sum of the dimensionalities of the inter-arrival and service time distribution representations. A numerically efficient algorithm with quadratic convergence rates based on the matrix sign function iterations is proposed to find the boundary conditions of the differential equation. The overall algorithm does not involve any transform domain calculations such as root finding or polynomial factorization, which are known to have potential numerical stability problems. Numerical examples are provided to demonstrate the effectiveness of the proposed approach. © 2004 Elsevier B.V. All rights reserved

Moments of Conditional Sojourn Times in Finite Capacity M/M/1/N-PS Processor Sharing Queues

Cataloged from PDF version of article.Moments of sojourn times conditioned on the length of an admitted job are derived for a finite capacity M/M/1/NPS processor sharing queue. The mean conditional sojourn time is given in closed form whereas an expression is provided for the conditional variance in such systems involving matrix-vector operations

Delay Analysis of Timer-Based Frame Coalescing in Energy Efficient Ethernet

Cataloged from PDF version of article.IEEE 802.3az, also known as Energy Efficient Ethernet (EEE), aims at reducing the energy consumption of an Ethernet link by placing it in sleep mode when the link is idle. Frame coalescing mechanism proposed for EEE is an effective means to increase the average idle time of the link, thus reducing the overhead stemming from sleep/wake transitions, but at the expense of increased frame delays. Therefore, it is imperative to quantify the energy-delay trade-off while employing frame coalescing. As opposed to existing delay models that focus only on the average delays, a simple but exact queuing model is introduced for timer-based frame coalescing to find the delay distribution when the frame arrival process is Poisson and frame lengths are generally distributed. An expression for average saving in power consumption is also provided

Role of ZIP14 (SLC39A14) gene histidine rich regions in neural tube defects

Neural tube defects (NTDs) comprise a group of congenital malformations that includes spina bifida, anencephaly, meningomyelocele and encephalocele. Reports have implicated zinc deficiency as one of the causative factors of NTDs. Both environmental and genetic factors are involved in the etiology of NTDs. Inadequate folate intake and nutritional deficiency are important environmental risk factors. The aim of this study was to determine the relation of a zinc related gene ZRT and IRT like protein 14 (ZIP14) and neural tube defects in Turkish patients. The case control study included seventy Turkish mothers who gave birth to NTD infants. Two hundred and thirty-nine healthy controls were consecutively selected without any congenital defects or familial NTD history. Following DNA extraction, PCR, SSCP and DNA sequencing analysis of exons of the ZIP14 gene were performed. Our data revealed that no relation of neural tube defects and ZIP14 was detected in Turkish NTD patients. Zinc deficiency have been reported as a risk factor for Turkish population and other possible zinc related gene defects may have importance.Keywords: Neural tube defects (NTDs); Zinc; ZIP1

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

A novel queue-aware wireless link adaptation mechanism and its fixed-point analytical model

A point-to-point (PTP) wireless link is studied that carries long-lived TCP flows and is controlled with active queue management (AQM). A cross-layer queue-aware adaptive modulation and coding (AMC)-based link adaptation (LA) mechanism is proposed for this wireless link to improve the TCP-level throughput relative to the case where AMC decisions are made based solely on the physical layer (PHY) parameters. The proposed simple-to-implement LA mechanism involves the use of an aggressive modulation and coding scheme (MCS) with high spectral efficiency and high block error rates when the queue occupancy exceeds a certain threshold, but otherwise a relatively conservative MCS with lower spectral efficiency and lower block error rates. A fixed-point analytical model is proposed to obtain the aggregate TCP throughput attained at this wireless link and the model is validated by ns-3 simulations. Numerical experimentation with the proposed analytical model applied to an IEEE 802.16-based wireless link demonstrates the effectiveness of the proposed queue-aware LA (QAWLA) mechanism in a wide variety of scenarios including cases where the channel information is imperfect. The impact of the choice of the queue occupancy threshold of QAWLA is extensively studied with respect to the choice of AQM parameters in order to provide engineering guidelines for the provisioning of the wireless link. © 2015, Ozturk and Akar

Running Multiple Instances of the Distributed Coordination Function for Air-time Fairness in Multi-Rate WLANs

Cataloged from PDF version of article.Conventional multi-rate IEEE 802.11 Wireless LANs (WLANs) are associated with the so-called performance anomaly to describe the phenomenon of high bit rate nodes being dragged down by slower nodes. This anomaly is known to be an impediment to obtaining high cumulative throughputs despite the employment of effective link adaptation mechanisms. To cope with the performance anomaly, air-time fairness has been proposed as an alternative to throughput fairness, the latter being a main characteristic of the IEEE 802.11 Distributed Coordination Function (DCF). In this paper, we propose a novel distributed air-time fair MAC (Medium Access Control) without having to change the operation of the conventional DCF. In the proposed MAC, each node in the system runs multiple instances of the conventional DCF back-off algorithm where the number of DCF instances for the nodes can be chosen in a distributed manner. Both analytical and simulation-based results are provided to validate the effectiveness of the proposed air-time fair MAC. © 2013 IEEE

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

MPLS Automatic Bandwidth Allocation via Adaptive Hysteresis

Cataloged from PDF version of article.MPLS automatic bandwidth allocation (or provisioning) refers to the process of dynamically updating the bandwidth allocation of a label switched path on the basis of actual aggregate traffic demand on this path. Since bandwidth updates require signaling, it is common to limit the rate of updates to reduce signaling costs. In this article, we propose a model-free asynchronous adaptive hysteresis algorithm for MPLS automatic bandwidth allocation under bandwidth update rate constraints. We validate the effectiveness of the proposed approach by comparing it against existing schemes in (i) voice and (ii) data traffic scenarios. The proposed method can also be used in more general GMPLS networks. (C) 2010 Elsevier B.V. All rights reserved

Exact Analysis of Offset-based Service Differentiation in Single-channel Multi-class OBS

Cataloged from PDF version of article.We study a multi-class optical burst switching (OBS) node using the horizon reservation scheme. Multiple traffic classes are differentiated using different offset times per class. Assuming Poisson burst arrivals and phase-type distributed burst lengths, we exactly solve for per-class blocking probabilities using the well-known theory of feedback Markov fluid queues