Buscador

Found 38 result(s)
Found 4 page(s)

Convergence of trajectories and optimal buffer sizing for MIMD congestion control

  • Zhang, Y.
  • Piunovskiy, A.
  • Ayesta, U.
  • Avrachenkov, K.
We study the interaction between the MIMD (Multiplicative Increase Multiplicative Decrease) congestion control and a bottleneck router with Drop Tail buffer. We consider the problem in the framework of deterministic hybrid models. We study conditions under which the system trajectories converge to limiting cycles with a single jump. Following that, we consider the problem of the optimal buffer sizing in the framework of multi-criteria optimization in which the Lagrange function corresponds to a linear combination of the average throughput and the average delay in the queue. As case studies, we consider the Slow Start phase of TCP New Reno and Scalable TCP for high speed networks. © 2009 Elsevier B.V. All rights reserved.
Project:


A modeling framework for optimizing the flow-level scheduling with time-varying channels

  • Ayesta, U.
  • Erausquin, M.
  • Jacko, P.
We introduce a comprehensive modeling framework for the problem of scheduling a finite number of finite-length jobs where the available service rate is time-varying. The main motivation comes from wireless data networks where the service rate of each user varies randomly due to fading. We employ recent advances on the restless bandit problem that allow us to obtain an opportunistic scheduling rule for the system without arrivals. When the objective is to minimize the mean number of users in the system or to minimize the mean waiting time, we obtain a priority-based policy which we call the "Potential Improvement" (PI) rule, since the priority index equals the ratio between the current available service rate and the expected potential improvement of the service rate. We also show that for certain objective functions, the index rule takes the form of known opportunistic scheduling rules like "Relatively Best" (RB) or "Proportionally Best" (PB). Thus our model provides a formal justification for the deployment of opportunistic scheduling rules in order to improve the flow-level performance in the presence of time-varying capacities. We further analyze the performance of the PI rule in the presence of randomly arriving users. When the service rates are constant, PI is equivalent to the cμ-rule, which is known to be optimal with any distribution of arrivals. Using a recent characterization for the stability region of flow-level scheduling rules under random arrivals, we show that PI achieves the maximum stability region. We perform numerical experiments in a wide range of scenarios and compare the performance of PI with other popular disciplines like RB, PB, Score-Based (SB) and the cμ-rule. Our results show that RB, PB, SB or the cμ-rule might outperform the others depending on the scenario, but regardless of this, the performance of PI is always superior or equivalent to the best of these opportunistic rules.
Project:


Convergence of trajectories and optimal buffer sizing for AIMD congestion control

  • Avrachenkov, K.
  • Ayesta, U.
  • Piunovskiy, A.
We study the interaction between the AIMD (Additive Increase Multiplicative Decrease) multi-socket congestion control and a bottleneck router with Drop Tail buffer. We consider the problem in the framework of deterministic hybrid models. First, we show that trajectories always converge to limiting cycles. We characterize the cycles. Necessary and sufficient conditions for the absence of multiple jumps in the same cycle are obtained. Then, we propose an analytical framework for the optimal choice of the router buffer size. We formulate this problem as a multi-criteria optimization problem, in which the Lagrange function corresponds to a linear combination of the average goodput and the average delay in the queue. Our analytical results are confirmed by simulations performed with MATLAB Simulink.
Project:


Asymptotically optimal parallel resource assignment with interference

  • Verloop, I.M.
  • Núñez-Queija, R.
Motivated by scheduling in cellular wireless networks and resource allocation in computer systems, we study a service facility with two classes of users having heterogeneous service requirement distributions. The aggregate service capacity is assumed to be largest when both classes are served in parallel, but giving preferential treatment to one of the classes may be advantageous when aiming at minimization of the number of users, or when classes have different economic values, for example. We set out to determine the allocation policies that minimize the total number of users in the system. For some particular cases we can determine the optimal policy exactly, but in general this is not analytically feasible. We then study the optimal policies in the fluid regime, which prove to be close to optimal in the original stochastic model. These policies can be characterized by either linear or exponential switching curves. We numerically compare our results with existing approximations based on optimization in the heavy-traffic regime. By simulations we show that, in general, our simple computable switching-curve strategies based on the fluid analysis perform well.
Project:


Monotonicity properties for multi-class queueing systems

  • Verloop, I.M.
  • Ayesta, U.
  • Borst, S.
We study multi-dimensional stochastic processes that arise in queueing models used in the performance evaluation of wired and wireless networks. The evolution of the stochastic process is determined by the scheduling policy used in the associated queueing network. For general arrival and service processes, we give sufficient conditions in order to compare sample-path wise the workload and the number of users under different policies. This allows us to evaluate the performance of the system under various policies in terms of stability, the mean overall delay and the mean holding cost. We apply the general framework to linear networks, where users of one class require service from several shared resources simultaneously. For the important family of weighted α-fair policies, stability results are derived and monotonicity of the mean holding cost with respect to the fairness parameter α and the relative weights is established. In order to broaden the comparison results, we investigate a heavy-traffic regime and perform numerical experiments. In addition, we study a single-server queue with two user classes, and show that under Discriminatory Processor Sharing (DPS) or Generalized Processor Sharing (GPS) the mean overall sojourn time is monotone with respect to the ratio of the weights. Finally we extend the framework to obtain comparison results that cover the single-server queue with an arbitrary number of classes as well.
Project:


Optimal routing in parallel, non-observable queues and the price of anarchy revisited

  • Anselmi, J.
  • Gaujal, B.
We consider a network of parallel, non-observable queues and analyze the "price of anarchy", an index measuring the worst-case performance loss of a decentralized system with respect to its centralized counterpart in presence of non-cooperative users. Our analysis is undertaken from the new point of view where the router has the memory of previous dispatching choices, which significantly complicates the nature of the problem. In the regime where the demands proportionally grow with the network capacity, we provide a tight lower bound on the socially-optimal response time and a tight upper bound on the price of anarchy by means of convex programming. Then, we exploit this result to show, by simulation, that the billiard routing scheme yields a response time which is remarkably close to our lower bound, implying that billiards minimize response time. To study the added-value of non-Bernoulli routers, we introduce the "price of forgetting" and prove that it is bounded from above by two, which is tight in heavy-traffic. Finally, other structural properties are derived numerically for the price of forgetting. These claim that the benefit of having memory in the router is independent of the network size and heterogeneity, while monotonically depending on the network load only. These properties yield simple productforms well-approximating the socially-optimal response time.
Project:


Breast cancer dormancy can be maintained by small numbers of micrometastases

  • Willis, L.
  • Alarcon, T.
  • Elia, G.
  • Jones, J.L.
  • Wright, N.A.
  • Tomlinson, I.P.M.
  • Graham, T.A.
  • Page, K.M.
Late relapse of breast cancer can occur more than 25 years after primary diagnosis. During the intervening years between initial treatment and relapse, occult cancers are maintained in an apparent state of dormancy that is poorly understood. In this study, we applied a probabilistic mathematical model to long-term follow-up studies of postresection patients to investigate the factors involved in mediating breast cancer dormancy. Our results suggest that long-term dormancy is maintained most often by just one growth-restricted dangerous micrometastasis. Analysis of the empirical data by Approximate Bayesian Computation indicated that patients in dormancy have between 1 and 5 micrometastases at 10 years postresection, when they escape growth restriction with a half-life of <69 years and are >0.4 mm in diameter. Before resection, primary tumors seed at most an average of 6 dangerous micrometastases that escape from growth restriction with a half-life of at least 12 years. Our findings suggest that effective preventive treatments will need to eliminate these small numbers of micrometastases, which may be preangiogenic and nonvascularized until they switch to growth due to one oncogenic mutation or tumor suppressor gene inactivation. In summary, breast cancer dormancy seems to be maintained by small numbers of sizeable micrometastases that escape from growth restriction with a half-life exceeding 12 years.
Project:


Influence of electromechanical effects and wetting layers on band structures of AlN/GaN quantum dots and spin control

  • Prabhakar, S.
  • Melnik, R.
In a series of recent papers we demonstrated that coupled electromechanical effects can lead to pronounced contributions in band structure calculations of low dimensional semiconductor nanostructures (LDSNs) such as quantum dots (QDs), wires, and even wells. Some such effects are essentially nonlinear. Both strain and piezoelectric effects have been used as tuning parameters for the optical response of LDSNs in photonics, band gap engineering, and other applications. However, the influence of spin orbit effects in presence of external magnetic field on single and vertically coupled QD has been largely neglected in the literature. The electron spin splitting terms which are coupled to the magnetic field through the Pauli spin matrix in these QDs become important in the design of optoelectronic devices as well as in tailoring properties of QDs in other applications areas. At the same time, single and vertically stacked QDs are coupled with electromagnetic and mechanical fields which become increasingly important in many applications of LDSN-based systems, in particular, where spin splitting energy is important. These externally applied electric and magnetic fields as well as the separation between the vertically coupled QDs can be used as tuning parameters. Indeed, as electromagnetic and elastic effects are often significant in LDSNs, it is reasonable to expect that the externally applied magnetic fields oriented along a direction perpendicular to the plane of two-dimensional electron gas in the QDs may also be used as a tuning parameter in the application of light emitting diodes, logic devices, for example, OR gates, AND gates and others. In this paper, by using the fully coupled model of electroelasticity, we analyze the influence of these effects on optoelectronic properties of QDs. Results are reported for III-V type semiconductors with a major focus given to AlN/GaN based QD systems.
Project:


Numerical equilibrium analysis for structured consumer resource models

  • de Roos, A.M.
  • Diekmann, O.
  • Getto, P.
  • Kirkilionis, M.A.
In this paper, we present methods for a numerical equilibrium and stability analysis for models of a size structured population competing for an unstructured resource. We concentrate on cases where two model parameters are free, and thus existence boundaries for equilibria and stability boundaries can be defined in the (two-parameter) plane. We numerically trace these implicitly defined curves using alternatingly tangent prediction and Newton correction. Evaluation of the maps defining the curves involves integration over individual size and individual survival probability (and their derivatives) as functions of individual age. Such ingredients are often defined as solutions of ODE, i.e., in general only implicitly. In our case, the right-hand sides of these ODE feature discontinuities that are caused by an abrupt change of behavior at the size where juveniles are assumed to turn adult. So, we combine the numerical solution of these ODE with curve tracing methods. We have implemented the algorithms for "Daphnia consuming algae" models in C-code. The results obtained by way of this implementation are shown in the form of graphs.
Project:


Higher-order nonlinear electromechanical effects in wurtzite GaN/AlN quantum dots

  • Bahrami-Samani, M.
  • Patil, S.R.
  • Melnik, R.
As we demonstrated earlier, conventional mathematical models based on linear approximations may be inadequate in the analysis of properties of low-dimensional nanostructures and band structure calculations. In this work, a general three-dimensional axisymmetric coupled electromechanical model accounting for lattice mismatch, spontaneous polarization and higher-order nonlinear electrostriction effects has been applied to analyze properties of GaN/AlN quantum dots coupled with wetting layer. The generalized model that accounts for five independent electrostriction coefficients has been solved numerically via a finite-element implementation. The results, exemplified for truncated conical GaN/AlN quantum dots, demonstrate that the effect of nonlinear electrostriction in GaN/AlN nanoheterostructure quantum dots could be significant. In particular, the influence of nonlinear electromechanical effects on optoelectronic properties is highlighted by the results on band structure calculations based on a multiband effective mass theory.
Project:


Advanced search