Queue Length Asymptotics for Generalized Max-Weight Scheduling in the presence of Heavy-Tailed Traffic

We investigate the asymptotic behavior of the steady-state queue length distribution under generalized max-weight scheduling in the presence of heavy-tailed traffic. We consider a system consisting of two parallel queues, served by a single server. One of the queues receives heavy-tailed traffic, and the other receives light-tailed traffic. We study the class of throughput optimal max-weight-alpha scheduling policies, and derive an exact asymptotic characterization of the steady-state queue length distributions. In particular, we show that the tail of the light queue distribution is heavier than a power-law curve, whose tail coefficient we obtain explicitly. Our asymptotic characterization also contains an intuitively surprising result - the celebrated max-weight scheduling policy leads to the worst possible tail of the light queue distribution, among all non-idling policies. Motivated by the above negative result regarding the max-weight-alpha policy, we analyze a log-max-weight (LMW) scheduling policy. We show that the LMW policy guarantees an exponentially decaying light queue tail, while still being throughput optimal

Max-weight scheduling in networks with heavy-tailed traffic

We consider the problem of packet scheduling in a single-hop network with a mix of heavy-tailed and light-tailed traffic, and analyze the impact of heavy-tailed traffic on the performance of Max-Weight scheduling. As a performance metric we use the delay stability of traffic flows: a traffic flow is delay stable if its expected steady-state delay is finite, and delay unstable otherwise. First, we show that a heavy-tailed traffic flow is delay unstable under any scheduling policy. Then, we focus on the celebrated Max-Weight scheduling policy, and show that a light-tailed flow that conflicts with a heavy-tailed flow is also delay unstable. This is true irrespective of the rate or the tail distribution of the light-tailed flow, or other scheduling constraints in the network. Surprisingly, we show that a light-tailed flow can be delay unstable, even when it does not conflict with heavy-tailed traffic. Furthermore, delay stability in this case may depend on the rate of the light-tailed flow. Finally, we turn our attention to the class of Max-Weight-α scheduling policies; we show that if the α-parameters are chosen suitably, then the sum of the α-moments of the steady-state queue lengths is finite. We provide an explicit upper bound for the latter quantity, from which we derive results related to the delay stability of traffic flows, and the scaling of moments of steady-state queue lengths with traffic intensity

Inferring the neutron star equation of state from binary inspiral waveforms

The properties of neutron star matter above nuclear density are not precisely known. Gravitational waves emitted from binary neutron stars during their late stages of inspiral and merger contain imprints of the neutron-star equation of state. Measuring departures from the point-particle limit of the late inspiral waveform allows one to measure properties of the equation of state via gravitational wave observations. This and a companion talk by J. S. Read reports a comparison of numerical waveforms from simulations of inspiraling neutron-star binaries, computed for equations of state with varying stiffness. We calculate the signal strength of the difference between waveforms for various commissioned and proposed interferometric gravitational wave detectors and show that observations at frequencies around 1 kHz will be able to measure a compactness parameter and constrain the possible neutron-star equations of state.Comment: Talk given at the 12th Marcel Grossman Meeting, Paris, France, 12-18 Jul 200

Max-Weight Scheduling in Queueing Networks With Heavy-Tailed Traffic

We consider the problem of scheduling in a single-hop switched network with a mix of heavy-tailed and light-tailed traffic and analyze the impact of heavy-tailed traffic on the performance of Max-Weight scheduling. As a performance metric, we use the delay stability of traffic flows: A traffic flow is delay-stable if its expected steady-state delay is finite, and delay-unstable otherwise. First, we show that a heavy-tailed traffic flow is delay-unstable under any scheduling policy. Then, we focus on the celebrated Max-Weight scheduling policy and show that a light-tailed flow that conflicts with a heavy-tailed flow is also delay-unstable. This is true irrespective of the rate or the tail distribution of the light-tailed flow or other scheduling constraints in the network. Surprisingly, we show that a light-tailed flow can become delay-unstable, even when it does not conflict with heavy-tailed traffic. Delay stability in this case may depend on the rate of the light-tailed flow. Finally, we turn our attention to the class of Max-Weight-α scheduling policies. We show that if the α-parameters are chosen suitably, then the sum of the α-moments of the steady-state queue lengths is finite. We provide an explicit upper bound for the latter quantity, from which we derive results related to the delay stability of traffic flows, and the scaling of moments of steady-state queue lengths with traffic intensity.National Science Foundation (U.S.) (Grant CNS-0915988)National Science Foundation (U.S.) (Grant CCF-0728554)United States. Air Force. Office of Scientific Research. Multidisciplinary University Research Initiative (Grant W911NF-08- 1-0238

Iteration Stability for Simple Newtonian Stellar Systems

For an equation of state in which pressure is a function only of density, the analysis of Newtonian stellar structure is simple in principle if the system is axisymmetric, or consists of a corotating binary. It is then required only to solve two equations: one stating that the "injection energy", $\kappa$, a potential, is constant throughout the stellar fluid, and the other being the integral over the stellar fluid to give the gravitational potential. An iterative solution of these equations generally diverges if $\kappa$ is held fixed, but converges with other choices. We investigate the mathematical reason for this convergence/divergence by starting the iteration from an approximation that is perturbatively different from the actual solution. A cycle of iteration is then treated as a linear "updating" operator, and the properties of the linear operator, especially its spectrum, determine the convergence properties. For simplicity, we confine ourselves to spherically symmetric models in which we analyze updating operators both in the finite dimensional space corresponding to a finite difference representation of the problem, and in the continuum, and we find that the fixed-$\kappa$ operator is self-adjoint and generally has an eigenvalue greater than unity; in the particularly important case of a polytropic equation of state with index greater than unity, we prove that there must be such an eigenvalue. For fixed central density, on the other hand, we find that the updating operator has only a single eigenvector, with zero eigenvalue, and is nilpotent in finite dimension, thereby giving a convergent solution.Comment: 16 pages, 3 figure

Throughput Optimal Scheduling Over Time-Varying Channels in the Presence of Heavy-Tailed Traffic

We study the problem of scheduling over time varying links in a network that serves both heavy-tailed and light tailed traffic. We consider a system consisting of two parallel queues, served by a single server. One of the queues receives heavy-tailed traffic (the heavy queue), and the other receives light-tailed traffic (the light queue). The queues are connected to the server through time-varying ON/OFF links, which model fading wireless channels. We first show that the policy that gives complete priority to the light-tailed traffic guarantees the best possible tail behavior of both queue backlog distributions, whenever the queues are stable. However, the priority policy is not throughput maximizing, and can cause undesirable instability effects in the heavy queue. Next, we study the class of throughput optimal max-weight-α scheduling policies. We discover a threshold phenomenon, and show that the steady state light queue backlog distribution is heavy-tailed for arrival rates above a threshold value, and light-tailed otherwise. We also obtain the exact tail coefficient of the light queue backlog distribution under max-weight-α scheduling. Finally, we study a log-max-weight scheduling policy, which is throughput optimal, and ensures that the light queue backlog distribution is light-tailed.National Science Foundation (U.S.) (Grant CNS-1217048)National Science Foundation (U.S.) (Grant CNS-0915988)National Science Foundation (U.S.) (CMMI-1234062)United States. Army Research Office. Multidisciplinary University Research Initiative (Grant W911NF-08-1-0238

Measuring the neutron star equation of state with gravitational wave observations

We report the results of a first study that uses numerical simulations to estimate the accuracy with which one can use gravitational wave observations of double neutron star inspiral to measure parameters of the neutron-star equation of state. The simulations use the evolution and initial-data codes of Shibata and Uryu to compute the last several orbits and the merger of neutron stars, with matter described by a parametrized equation of state. Previous work suggested the use of an effective cutoff frequency to place constraints on the equation of state. We find, however, that greater accuracy is obtained by measuring departures from the point-particle limit of the gravitational waveform produced during the late inspiral. As the stars approach their final plunge and merger, the gravitational wave phase accumulates more rapidly for smaller values of the neutron star compactness (the ratio of the mass of the neutron star to its radius). We estimate that realistic equations of state will lead to gravitational waveforms that are distinguishable from point particle inspirals at an effective distance (the distance to an optimally oriented and located system that would produce an equivalent waveform amplitude) of 100 Mpc or less. As Lattimer and Prakash observed, neutron-star radius is closely tied to the pressure at density not far above nuclear. Our results suggest that broadband gravitational wave observations at frequencies between 500 and 1000 Hz will constrain this pressure, and we estimate the accuracy with which it can be measured. Related first estimates of radius measurability show that the radius can be determined to an accuracy of ~1 km at 100 Mpc.Comment: 12 pages, 5 figures, to be submitted to Phys. Rev.

Neutron star equation of state via gravitational wave observations

Gravitational wave observations can potentially measure properties of neutron star equations of state by measuring departures from the point-particle limit of the gravitational waveform produced in the late inspiral of a neutron star binary. Numerical simulations of inspiraling neutron star binaries computed for equations of state with varying stiffness are compared. As the stars approach their final plunge and merger, the gravitational wave phase accumulates more rapidly if the neutron stars are more compact. This suggests that gravitational wave observations at frequencies around 1 kHz will be able to measure a compactness parameter and place stringent bounds on possible neutron star equations of state. Advanced laser interferometric gravitational wave observatories will be able to tune their frequency band to optimize sensitivity in the required frequency range to make sensitive measures of the late-inspiral phase of the coalescence.Comment: Talk given at the 13th Conference on Recent Developments in Gravity (NEB XIII), Thessaloniki, Greece, 4-6 Jun 200

Small-bowel necrosis complicating a cytomegalovirus-induced superior mesenteric vein thrombosis in an immunocompetent patient: a case report

<p>Abstract</p> <p>Introduction</p> <p>Superior mesenteric venous thrombosis as a result of acute cytomegalovirus infection is rare, with only a few cases reported in the literature.</p> <p>Case presentation</p> <p>We present the case of a 40-year-old Caucasian man who was admitted to our hospital with a 5-day history of fever. His serological test and pp65 antigen detection of cytomegalovirus were positive, suggesting acute infection. On the sixth day after his admission, the patient complained of acute, progressive abdominal pain. Abdominal computed tomography revealed acute superior mesenteric venous thrombosis. An emergency laparotomy showed diffuse edema and ischemic lesions of the small bowel and its associated mesentery with a 50-cm-long segmental infarction of the proximal jejunum. An extensive enterectomy of about 100 cm of jejunum that included the necrotic segment was performed, followed by an end-to-end anastomosis. Anti-coagulation therapy was administered pre-operatively in the form of small-fractionated heparin and continued postoperatively. The patient had an uneventful recovery and was discharged on the 11th postoperative day.</p> <p>Conclusion</p> <p>Acute cytomegalovirus infection can contribute to the occurrence of mesenteric venous thrombosis in immunocompetent patients. It is important for physicians and internists to be aware of the possible thrombotic complications of cytomegalovirus infection. A high level of clinical suspicion is essential to successfully treat a potentially lethal condition such as superior mesenteric venous thrombosis.</p