Software rejuvenation and resource reservation policies for optimizing server resource availability using cyclic nonhomogeneous Markov chains

Scheduling control for a single-server queue with I customer classes and reneging is considered, with linear holding or reneging cost. An asymptotically optimal (AO) policy in heavy traffic is identified where classes are prioritized according to a workload-dependent dynamic index rule. Denote by ci, μi, and θi, i ∈ ℐ := {1, …, I} the queue length cost, service rate, and reneging rate, for class-i customers. Then, a relabeling of the classes and a partition 0 = w0 < w1 < ⋯ < wK = ∞, K ≤ I are identified such that the policy acts to always assign least priority to the class i when the rescaled workload is in the interval [wi−1, wi). The relabeling is such that when workload is withing the lowest [resp., highest] interval [wi−1, wi), the least priority class is the one with smallest cμ [resp., greatest θ] value. This result stands in sharp contrast to known fluid-scale results where it is AO to prioritize by the fixed cμ/θ index. One of the technical challenges is the discontinuity of the limiting queue length process under optimality. Discontinuities occur whenever the workload reaches one of the levels wi.

We present a representation of the inverse of a matrix for solving large sparse systems of linear algebraic equations $Ax = b$, that arises from the bordering method. We analyse the properties of the method for sparse matrices permuted to a suitable form. The relevant feature of the method is that it creates nonzero elements only in spike columns above the main diagonal. For an $n \times n$ matrix A with $\tau _0 $ nonzero elements, the number of nonzero elements in the representation of the inverse satisfies the inequality $\tau < \tau _0 + h \cdot n$, where h is a certain constant. It is proved that, under suitable assumptions, $h\leqq \log _2 s + 1$, where s is the number of spikes. The computation of the hierarchical form of the inverse requires at most $h \cdot \tau $ additions and $h \cdot \tau $ multiplications. For the known representation of the inverse, the solution of the system $Ax = b$ requires no more than $\tau - n$ additions and $\tau $ multiplications.

Localized method of fundamental solutions for solving two-dimensional Laplace and biharmonic equations

We investigate the sparse underdetermined system of linear algebraic equations that arise in applications to the traffic in the network. We consider the technological and informational aspects of building a general and unique solution of the sparse linear systems in the Sensor Location Problem for the graph.

Application of wavelet analysis to an inverse problem in eddy current testing

The application of the finite element method invariably involves the solution of large sparse systems of linear algebraic equations, and the solution of these systems often represents a significant or even dominant component of the total cost of applying the method. The object of this paper is to describe and relate various sparse matrix techniques which have been developed to make the solution of these equations more efficient.KeywordsStiffness MatrixSparse MatrixDiagonal BlockInterior NodeStorage SchemeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Introduction. Kron [1] has developed a technique for tearing large, sparse linear systems of algebraic equations into smaller systems, then putting the solutions of these smaller systems together to form the solution of the original problem. This can result in a great savings over solving the whole system in one piece. The trick is to find where to tear so that on the one hand the remaining pieces are small and easily solvable, but on the other hand not so much violence is done to the equations so that the task of putting their solutions back together becomes too difncult. Kron's pro? cedure for solving the pieces and putting their solutions together is based upon representing systems of equations as electric networks. He makes his choice of where to tear from his insight into these networks and the physical processes the equations represent. In the hands of someone such as Kron who has an understanding of the methods and good insight into the prob? lem, this technique has had outstanding success. The widespread use of Kron's technique has perhaps been limited severely for lack of practitioners skilled in this art of determining effective ways of tearing specific problems. Many problems are too large to submit to such insight. It is the purpose of this paper to contribute to the development of procedures which can be performed on a computer for analyzing the structures of the systems of equations themselves as an aid in choosing how to break them up for easier solution. The methods developed here require only that we consider what variables occur in each equation, but not how they appear. Thus, the tech? niques are not limited to linear systems.

The localized method of fundamental solutions (LMFS) is a domain-type, meshless numerical method. Compared with numerical methods that have a high grid dependence, it does not require grid generation and numerical integration, so it can effectively improve computational efficiency and avoid complex integration processes. Moreover, it is formed using the traditional method of fundamental solutions (MFS) and the localization approach. Previous studies have shown that the MFS may produce a dense and ill-conditioned matrix. However, the proposed LMFS can yield a sparse system of linear algebraic equations, so it is more suitable and effective in solving complicated engineering problems. In this article, LMFS was used to solve eigenfrequency problems in electromagnetic waves, which were controlled using two-dimensional Helmholtz equations. Additionally, the resonant frequencies of the eigenproblem were determined by the response amplitudes. In order to determine the eigenfrequencies, LMFS was applied for solving a sequence of inhomogeneous problems by introducing an external source. Waveguides with different shapes were analyzed to prove the stability of the present LMFS in this paper.

Krylov subspace methods based on short recurrences such as CGL or MINRES represent an attractive way of solving large and sparse systems of linear algebraic equations. Loss of orthogonality in the underlying Lanczos process delays significantly their convergence in finite-precision computation, whose connection to exact computation is still not fully understood. In this paper, we exploit the idea of simultaneous comparison of finite-precision and exact computations for CGL and MINRES, by taking advantage of their relationship valid also in finite-precision arithmetic. In particular, we show that finite-precision CGL residuals and Lanczos vectors have to be aggregated over the intermediate iterations to form a counterpart to vectors from the exact computation. Influence of stagnation in exact MINRES computation is also discussed. Obtained results are supported by numerical experiments.

The paper considers a classical M/M/1 queue with two priority classes under a preemptive priority discipline. Based on the performance measures of White and Christie [14], the paper studies the optimal pricing policy of the server who is an individual profit maximizer when the customers adopt their respective equilibrium arrival rate, then discusses the service rate control problem from the perspective of social welfare maximization. Because of the complexity of the model, it's intractable to theoretically analyze the queueing system in depth. In the section of example analyses, two numerical examples are presented, on the one hand to give the specifically optimal pricing policy and service rate control policy, and on the other hand to conduct some sensitivity analyses for some important parameters.

Dynamic Spectrum Access (DSA) has the potential to vastly improve spectrum utilizations among heterogeneous networks. We present a continuous-time Markov chain (CT-MC) model to analyze the performance of three co-located cognitive systems with various priority classes and bandwidth requirements. The maximum spectrum utilization and minimum blocking probability are derived in a one-channel band scenario. A channel packing scheme (CPS) is then proposed in a multiple-channel band scenario. This scheme packs users of smaller bandwidth requirements in clusters, in order to alleviate the unnecessary blockage to users of larger bandwidth requirements. Numerical results show that the system can benefit from CPS in terms of blocking probability, spectrum utilization and overall failure probability.

In previous work we presented the Triage protocol, an end-to-end (E2E) QoS approach, where packet scheduling is biased by priority class, the severity of distress in meeting E2E QoS goals, and the likelihood of meeting those goals if service rates are altered. In this work, we present improvements to the heuristics used to determine the Triage distress in the per-hop behavior, simulation results showing a 22% bandwidth gain through use of the Triage QoS protocol. Finally, we also show that significant gains are obtained even under high mobility conditions..

A significant amount of recent research has been focused on the stability of multiclass open networks of queues (MONQs). It has been shown that these networks may be unstable under various queueing disciplines even when at each one of the nodes the arrival rate is less than the service rate. Clearly, in such cases the expected delay and the expected number of customers in the system are infinite. In this paper we propose a new class of scheduling rules that can be used in multiclass queueing networks. We refer to this class as the stable shortfall-based priority (SSBP) rules. This SSBP class itself belongs to a larger class of rules, which we refer to as the shortfall-based priority (SBP) rules. SBP is a generalization of the standard non-preemptive priority rule in which customers of the same priority class are served first-come, first-served (FCFS). Rules from SBP can mimic FCFS as well as the so-called strict or head-of-the-line priority disciplines. We show that the use of any rule from the SSBP class ensures stability in a broad class of MONQs found in practice. We proceed with the construction of a sample path inequality for the work done by an SSBP server and show how this inequality can be used to derive upper bounds for the delay when service times are bounded. Bounds for the expected delay of each class of customers in an MONQ are then obtained under the assumptions that the external arrival processes have i.i.d. interarrival times, the routings are deterministic and the service times at each step of the route are bounded. In order to derive these bounds for the average delay in an MONQ we make use of some of the classical ideas of Kingman.

We study an authentication system that receives requests from different types of users. A centralized controller must assign an authentication method to each request, considering the type, the state of the system and the characteristics of several available methods. Each authentication method has different capacity, service rate, level of security, level of usability and operating cost. We seek to optimize security, usability and operating cost, simultaneously by assigning authentication methods dynamically, in real time. To do this, we model the system as a network of parallel multi-server queues, where each queue represents an authentication method and each customer represents a request. We use two different approaches to handle the multiple objectives: a weighted total cost function, and treating security and latency as constraints while minimizing operating cost. We employ constrained and unconstrained Markov decision processes to determine the structure of policies that effectively balance these three objectives. We conclude that if there are infinitely many servers for each authentication method, then the optimal policy is static. We also show that if one method has finite capacity, then the optimal policy is of trunk reservation form. Our results regarding the structure of the optimal policy are consistent for both modeling approaches. Our work shows that optimal policies have intuitive, easy-to-implement structures that are useful in practice. Under certain assumptions, we provide a straightforward way to obtain an optimal policy. We also offer strategies to use our models to explore non-dominated solutions over the three objective functions.

Variable bit-rate (VBR) compressed video traffic is expected to be a significant component of the traffic mix in integrated services networks. This traffic is hard to manage because it has strict delay and loss requirements while simultaneously exhibiting burstiness at multiple time scales. We show that burstiness over long time scales, in conjunction with resource reservation using one-shot traffic descriptors, can substantially degrade the loss rate, end-to-end delay, and statistical multiplexing gain of a connection. We use large-deviation theory to model the performance of multiple time-scale traffic and to motivate the design of renegotiated constant bit rate (RCBR) service. Sources using RCBR service are presented with an abstraction of a fixed-size buffer which is drained at a constant rate. They may renegotiate the drain rate to match their workload. Because all traffic entering the network is constant bit-rate (CBR), RCBR requires minimal buffering and scheduling support in switches. We show that the service is suitable for both stored and online video sources. An RCBR source must decide when to renegotiate its service rate and what the new service rate should be. We present: (1) an algorithm to compute the optimal renegotiation schedule for stored (offline) traffic and (2) a heuristic to approximate the optimal schedule for online traffic. We also discuss measurement-based admission control (MBAC) for RCBR traffic. Simulation experiments show that RCBR is able to extract almost all of the statistical multiplexing gain available by exploiting slow time-scale variations in traffic. Moreover, simple admission control schemes are sufficient to keep the renegotiation failure probability below a small threshold while still offering high link utilization. Thus, we believe that RCBR is a simple, practical, and effective service for carrying multiple time-scale traffic.