Stackelberg Strategies for Selfish Routing in General Multicommodity Networks

A natural generalization of the selfish routing setting arises when some of the users obey a central coordinating authority, while the rest act selfishly. Such behavior can be modeled by dividing the users into an α fraction that are routed according to the central coordinator’s routing strategy (Stackelberg strategy), and the remaining 1−α that determine their strategy selfishly, given the routing of the coordinated users. One seeks to quantify the resulting price of anarchy, i.e., the ratio of the cost of the worst traffic equilibrium to the system optimum, as a function of α. It is well-known that for α=0 and linear latency functions the price of anarchy is at most 4/3 (J. ACM 49, 236–259, 2002). If α tends to 1, the price of anarchy should also tend to 1 for any reasonable algorithm used by the coordinator. We analyze two such algorithms for Stackelberg routing, LLF and SCALE. For general topology networks, multicommodity users, and linear latency functions, we show a price of anarchy bound for SCALE which decreases from 4/3 to 1 as α increases from 0 to 1, and depends only on α. Up to this work, such a tradeoff was known only for the case of two nodes connected with parallel links (SIAM J. Comput. 33, 332–350, 2004), while for general networks it was not clear whether such a result could be achieved, even in the single-commodity case. We show a weaker bound for LLF and also some extensions to general latency functions. The existence of a central coordinator is a rather strong requirement for a network. We show that we can do away with such a coordinator, as long as we are allowed to impose taxes (tolls) on the edges in order to steer the selfish users towards an improved system cost. As long as there is at least a fraction α of users that pay their taxes, we show the existence of taxes that lead to the simulation of SCALE by the tax-payers. The extension of the results mentioned above quantifies the improvement on the system cost as the number of tax-evaders decreases. Research of G. Karakostas supported by an NSERC Discovery Grant and MITACS. Research of S. Kolliopoulos partially supported by the University of Athens under the project Kapodistrias.     

Effects of time and sampling location on concentrations of β-hydroxybutyric acid in dairy cows

Two trials were conducted to examine factors potentially influencing the measurement of blood β-hydroxybutyric acid (BHBA) in dairy cows. The objective of the first trial was to study effects of sampling time on BHBA concentration in continuously fed dairy cows. Furthermore, we determined test characteristics of a single BHBA measurement at a random time of the day to diagnose subclinical ketosis considering commonly used cut-points (1.2 and 1.4 mmol/L). Finally, we set out to evaluate if test characteristics could be enhanced by repeating measurements after different time intervals. During 4 herd visits, a total of 128 cows (8 to 28 d in milk) fed 10 times daily were screened at 0900 h and preselected by BHBA concentration. Blood samples were drawn from the tail vessels and BHBA concentrations were measured using an electronic BHBA meter (Precision Xceed, Abbott Diabetes Care Ltd., Witney, UK). Cows with BHBA concentrations ≥0.8 mmol/L at this time were enrolled in the trial (n = 92). Subsequent BHBA measurements took place every 3 h for a total of 8 measurements during 24 h. The effect of sampling time on BHBA concentrations was tested in a repeated-measures ANOVA repeating sampling time. Sampling time did not affect BHBA concentrations in continuously fed dairy cows. Defining the average daily BHBA concentration calculated from the 8 measurements as the gold standard, a single measurement at a random time of the day to diagnose subclinical ketosis had a sensitivity of 0.90 or 0.89 at the 2 BHBA cut-points (1.2 and 1.4 mmol/L). Specificity was 0.88 or 0.90 using the same cut-points. Repeating measurements after different time intervals improved test characteristics only slightly. In the second experiment, we compared BHBA concentrations of samples drawn from 3 different blood sampling locations (tail vessels, jugular vein, and mammary vein) of 116 lactating dairy cows. Concentrations of BHBA differed in samples from the 3 sampling locations. Mean BHBA concentration was 0.3 mmol/L lower when measured in the mammary vein compared with the jugular vein and 0.4 mmol/L lower in the mammary vein compared with the tail vessels. We conclude that to measure BHBA, blood samples of continuously fed dairy cows can be drawn at any time of the day. A single measurement provides very good test characteristics for on-farm conditions. Blood samples for BHBA measurement should be drawn from the jugular vein or tail vessels; the mammary vein should not be used for this purpose.     

Expanding the dairy herd in pasture-based systems: The role of sexed semen use in virgin heifers and lactating cows

A model was developed to examine the effects of sexed semen use in virgin heifers and lactating cows on replacement heifer numbers and rate of herd expansion in a seasonal dairy production system. Five separate herds were established according to the type of semen used: conventional frozen-thawed (Conv), sexed fresh semen used in lactating cows for the first 3 wk of the breeding season (SFre1), sexed frozen-thawed semen used in lactating cows for the first 3 wk of the breeding season (SFro1), sexed fresh semen used in lactating cows for the first 6 wk of the breeding season (SFre2), or sexed frozen-thawed semen used in lactating cows for the first 6 wk of the breeding season (SFro2). In the SFro1, SFre1, SFro2, and SFre2 herds, sexed semen was used for the first and second artificial insemination in virgin heifers. Pregnancy rates achieved with sexed fresh and sexed frozen-thawed semen were assumed to be 94 and 75% of those achieved with conventional frozen-thawed semen, respectively. Initial herd size was 100 cows, which was maintained for the first 2 yr of the 15-yr simulation, after which all available replacement heifers were retained to facilitate herd expansion. Two different scenarios of land availability were examined for each of the 5 herds: land available allowed expansion to a maximum herd size of 150 cows (S1), or land available allowed expansion to a maximum herd size of 300 cows (S2). Once maximum herd size was reached, sexed semen use was discontinued and all excess heifer calves were sold at 1 mo old. All capital expenditure associated with expansion was financed with a 15-yr loan. Each of the 10 different options was evaluated in terms of annual farm profit, annual cash flow, and total discounted net profit. The use of fresh sexed semen generated more replacement heifers, leading to faster herd expansion compared with frozen-thawed sexed semen and conventional frozen-thawed semen. Maximum herd size under S1 was reached in yr 5, 5, 4, 5, and 7 for the SFre1, SFro1, SFre2, SFro2, and Conv herds, respectively. Under S2, maximum herd size was reached in yr 8, 10, 7, 9, and 14 for the SFre1, SFro1, SFre2, SFro2, and Conv herds, respectively. Total discounted net profit under S1 for the SFre2 herd was €4,130, €38,869, €47,231, and €52,089 greater compared with the SFre1, SFro1, Conv, and SFro2 herds, respectively. Under S2, discounted net profit for the SFre2 herd was €44,204, €255,524, €280,373, and €325,815 greater compared with the SFre1, SFro1, SFro2, and Conv herds, respectively. The negative effects of the sexed frozen-thawed semen on herd fertility reduced farm profitability and will prevent its widespread use in lactating cows.     

Optimal replacement policies for dairy cows based on daily yield measurements

Markov decision processes (MDP) with finite state and action space have often been used to model sequential decision making over time in dairy herds. However, the length of each stage has been at least 1 mo, resulting in models that do not support decisions on a daily basis. The present paper describes the first step of developing an MDP model that can be integrated into a modern herd management system. A hierarchical MDP was formulated for the dairy cow replacement problem with stage lengths of 1 d. It can be used to assist the farmer in replacement decisions on a daily basis and is based on daily milk yield measurements that are available in modern milking systems. Bayesian updating was used to predict the performance of each cow in the herd and economic decisions were based on the prediction. Moreover, parameters in the model were estimated using data records of the specific herd under consideration. This includes herd-specific lactation curves.     

Aflatoxin M1 and ochratoxin A in raw bulk milk from French dairy herds

Mycotoxins in milk are a public health concern and have to be regularly monitored. A survey on the presence of aflatoxin M₁ (AFM₁) and ochratoxin A (OTA) in raw bulk milk was conducted in 2003 in the northwest of France, the main French milk-producing basin. Randomly selected farms (n = 132) were characterized by a diet based on corn silage and containing a large proportion of on-farm produced cereals, feeding sources that are frequently contaminated by mycotoxins. Farms were surveyed twice in winter and in summer. At each sampling time, a trained surveyor completed a questionnaire recording farm management procedures and production traits. The AFM₁ was found in 3 out of 264 samples but at levels (26 ng/L or less) that are below the European legislation limit of 50 ng/L. Traces of AFM₁ (less than 8 ng/L) were also found in 6 other samples. The OTA was detected in 3 samples also at low levels, 5 to 8 ng/L. Farms that tested positive to the presence of mycotoxins, 12 in total including 6 farms that had traces of AFM₁, differed from negative farms by a more extensive use of total mixed rations, 58 vs. 27%. In addition, the positive farms tended to have lower milk yields. Although the incidence of milk contamination with AFM₁ and OTA at the farm level was low during the period studied, production and management data from the surveyed farms suggest a link between feeding management practices and mycotoxin contamination.     

基于磷虾群算法的并网电动汽车功率优化分配

为提高并网电动汽车(EV)集群的功率优化分配效率,提出基于磷虾群算法的EV集群并网两阶段功率高效分配策略。考虑用户的需求差异,将并网EV细化为不可调度集及可调度集,分别建立充放电控制模型,提出可调度集EV的优先权评估指标。采用动态自适应权重策略及余弦递减步长演进策略改进磷虾群(KH)算法,将可调度集EV的优先权映射为迭代算法的演变步长,通过两阶段交互迭代实现并网EV集群的功率高效分配。仿真实验验证了模型的可行性以及所提策略的高效性。     

基于DGA特征量优选与改进磷虾群算法优化支持向量机的变压器故障诊断模型

针对单一的特征气体或特征气体比值作为DGA特征量无法全面反映变压器故障分类的问题,本文从混合DGA特征量中优选出一组DGA新特征组合为输入,建立改进磷虾群(Improved Krill Herd,IKH)算法优化支持向量机(Support vector machine,SVM)的变压器故障诊断模型进行故障诊断。将SVM的c和s与11种候选特征量进行二进制编码,利用遗传算法结合支持向量机对DGA特征量进行优选,得到一组最优DGA新特征组合;利用IKH算法对SVM的参数进行优化,同时结合交叉验证原理构建IKH算法优化SVM的变压器故障诊断模型。基于IEC TC 10的诊断结果表明：与DGA全数据、三比值特征量相比,新DGA特征组合的故障诊断准确率分别高出10.14%和30.2%;IKHSVM准确率也要高于标准SVM和GASVM(分别为73.87%、81.13%和86.27%),说明该方法能有效诊断变压器故障。     

Management,operational, animal health,and economic characteristics of large dairy herds in 4 states in the Upper Midwest of the United States

Recent trends in dairy farm structure in the United States have included a decreasing number of farms, although farm size has increased, especially the share of milk production from very large herds (>2,500 cows). The objectives of this observational study were to describe common management practices; to characterize labor and operational structure; to measure some aspects of animal health, including lameness, hock lesions, mortality, and mastitis incidence; and to summarize cost of production on farms with more than 2,500 cows in 4 states in the Upper Midwest of the United States. The study included 15 dairy farms in Minnesota, Wisconsin, Iowa, and South Dakota. Farms were visited twice, once each year, and on-farm herd records were collected for those 2 yr. On-farm herd records were used to investigate mortality, culling, pregnancy rate, and clinical mastitis incidence. At least 1 high-producing pen of mature cows and 1 pen of fresh cows were scored for locomotion. Likewise, at least 1 pen of high-producing mature cows was scored for cleanliness and hock lesions. Median herd size was 3,975 cows (range = 2,606–13,266). Milk sold per employee was 1,120,745 kg and the number of cows per employee was 105. Eighty percent of the farms had Holstein cows, 13% had Jersey, and 7% had Jersey-Holstein crosses. All farms used artificial insemination as the sole form of breeding and 100% of the farms used hormonal synchronization or timed artificial insemination programs in their reproductive protocols; 21-d pregnancy rate was 21.7%. Median lameness prevalence was 18.3% and median severe lameness prevalence was 5.1%. Median hock lesion prevalence was 17.4% and median severe hock lesion prevalence was 1.9%; mortality rate was 7.4%. Clinical mastitis incidence was 62.5 cases per 100 cow-years. Feed costs accounted for approximately 53% of the total cost of producing milk, followed by labor at 11%, interest and depreciation expenses at 10%, and replacement costs at 9.5%. Herds in the top 50th percentile for profitability had a net income of $2.40 per hundredweight of milk sold compared with $0.95 per hundredweight for herds in the bottom 50th percentile. Although results of this study were helpful in understanding how large dairy systems operate in the Upper Midwest, more research is yet needed with a larger number of farms and wider variety of management practices to identify factors within these large farms that promote optimal animal health and profitability.