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

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

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

The prevalence and distribution of the amyloidogenic transthyretin (TTR) V122I allele in Africa

Transthyretin (TTR) pV142I (rs76992529-A) is one of the 113 variants in the human TTR gene associated with systemic amyloidosis. It results from a G to A transition at a CG dinucleotide in the codon for amino acid 122 of the mature protein (TTR V122I). The allele frequency is 0.0173 in African Americans

Genome landscapes and bacteriophage codon usage

Across all kingdoms of biological life, protein-coding genes exhibit unequal usage of synonmous codons. Although alternative theories abound, translational selection has been accepted as an important mechanism that shapes the patterns of codon usage in prokaryotes and simple eukaryotes. Here we analyze patterns of codon usage across 74 diverse bacteriophages that infect E. coli, P. aeruginosa and L. lactis as their primary host. We introduce the concept of a `genome landscape,' which helps reveal non-trivial, long-range patterns in codon usage across a genome. We develop a series of randomization tests that allow us to interrogate the significance of one aspect of codon usage, such a GC content, while controlling for another aspect, such as adaptation to host-preferred codons. We find that 33 phage genomes exhibit highly non-random patterns in their GC3-content, use of host-preferred codons, or both. We show that the head and tail proteins of these phages exhibit significant bias towards host-preferred codons, relative to the non-structural phage proteins. Our results support the hypothesis of translational selection on viral genes for host-preferred codons, over a broad range of bacteriophages.Comment: 9 Color Figures, 5 Tables, 53 Reference

Human candidate gene polymorphisms and risk of severe malaria in children in Kilifi, Kenya: a case-control association study

Background: Human genetic factors are important determinants of malaria risk. We investigated associations between multiple candidate polymorphisms—many related to the structure or function of red blood cells—and risk for severe Plasmodium falciparum malaria and its specific phenotypes, including cerebral malaria, severe malaria anaemia, and respiratory distress. Methods: We did a case-control study in Kilifi County, Kenya. We recruited as cases children presenting with severe malaria to the high-dependency ward of Kilifi County Hospital. We included as controls infants born in the local community between Aug 1, 2006, and Sept 30, 2010, who were part of a genetics study. We tested for associations between a range of candidate malaria-protective genes and risk for severe malaria and its specific phenotypes. We used a permutation approach to account for multiple comparisons between polymorphisms and severe malaria. We judged p values less than 0·005 significant for the primary analysis of the association between candidate genes and severe malaria. Findings: Between June 11, 1995, and June 12, 2008, 2244 children with severe malaria were recruited to the study, and 3949 infants were included as controls. Overall, 263 (12%) of 2244 children with severe malaria died in hospital, including 196 (16%) of 1233 with cerebral malaria. We investigated 121 polymorphisms in 70 candidate severe malaria-associated genes. We found significant associations between risk for severe malaria overall and polymorphisms in 15 genes or locations, of which most were related to red blood cells: ABO, ATP2B4, ARL14, CD40LG, FREM3, INPP4B, G6PD, HBA (both HBA1 and HBA2), HBB, IL10, LPHN2 (also known as ADGRL2), LOC727982, RPS6KL1, CAND1, and GNAS. Combined, these genetic associations accounted for 5·2% of the variance in risk for developing severe malaria among individuals in the general population. We confirmed established associations between severe malaria and sickle-cell trait (odds ratio [OR] 0·15, 95% CI 0·11–0·20; p=2·61 × 10−58), blood group O (0·74, 0·66–0·82; p=6·26 × 10−8), and –α3·7-thalassaemia (0·83, 0·76–0·90; p=2·06 × 10−6). We also found strong associations between overall risk of severe malaria and polymorphisms in both ATP2B4 (OR 0·76, 95% CI 0·63–0·92; p=0·001) and FREM3 (0·64, 0·53–0·79; p=3·18 × 10−14). The association with FREM3 could be accounted for by linkage disequilibrium with a complex structural mutation within the glycophorin gene region (comprising GYPA, GYPB, and GYPE) that encodes for the rare Dantu blood group antigen. Heterozygosity for Dantu was associated with risk for severe malaria (OR 0·57, 95% CI 0·49–0·68; p=3·22 × 10−11), as was homozygosity (0·26, 0·11–0·62; p=0·002). Interpretation: Both ATP2B4 and the Dantu blood group antigen are associated with the structure and function of red blood cells. ATP2B4 codes for plasma membrane calcium-transporting ATPase 4 (the major calcium pump on red blood cells) and the glycophorins are ligands for parasites to invade red blood cells. Future work should aim at uncovering the mechanisms by which these polymorphisms can result in severe malaria protection and investigate the implications of these associations for wider health. Funding: Wellcome Trust, UK Medical Research Council, European Union, and Foundation for the National Institutes of Health as part of the Bill & Melinda Gates Grand Challenges in Global Health Initiative

A new approach for identifying non-pathogenic mutations. An analysis of the cystic fibrosis transmembrane regulator gene in normal individuals

Given q as the global frequency of the alleles causing a disease, any allele with a frequency higher than q minus the cumulative frequency of the previously known disease-causing mutations (threshold) cannot be the cause of that disease. This principle was applied to the analysis of cystic fibrosis transmembrane conductance regulator (CFTR) mutations in order to decide whether they are the cause of cystic fibrosis. A total of 191 DNA samples fl-om random individuals from Italy, France, and Spain were investigated by DGGE (denaturing gradient gel electrophoresis) analysis of all the coding and proximal non-coding regions of the gene. The mutations detected by DGGE were identified by sequencing. The sample size was sufficient to select essentially all mutations with a frequency of at least 0.01. A total of 46 mutations was detected, 20 of which were missense mutations. Four new mutations were identified: 1341+28 C/T, 2082 C/T, L1096R, and I1131V. Thirteen mutations (125 G/C, 875+40 A/G, TTGAn, IVS8-6 5T, IVS8-6 9T, 1525-61 A/G, M470V, 2693 T/G, 3061-65 C/A, 4002 A/G, 4521 G/A, IVS8 TG10, IVS8 TG12) were classified as non-CF-causing alleles on the basis of their frequency. The remaining mutations have a cumulative frequency far exceeding q; therefore, most of them cannot be CF-causing mutations. This is the first random survey capable of detecting all the polymorphisms of the coding sequence of a gene