A diffusion-based analysis of a multi-class road traffic network

This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows on the basis of conservation laws that incorporate the macroscopic fundamental diagram (a functional relationship between vehicle density and flow). Our setup is capable of handling multiple types of vehicle densities, with general macroscopic fundamental diagrams, on a network with arbitrary topology. Interpreting our system as a spatial population process, we derive, under a natural scaling, fluid and diffusion limits. More specifically, the vehicle density process can be approximated with a suitable Gaussian process, which yield accurate normal approximations to the joint (in the spatial and temporal sense) vehicle density process. The corresponding means and variances can be computed efficiently. Along the same lines, we develop an approximation to the vehicles' travel-time distribution between any given origin and destination pair. Finally, we present a series of numerical experiments that demonstrate the accuracy of the approximations and illustrate the usefulness of the results

Diffusion limits for a Markov modulated binomial counting process

In this paper we study limit behavior for a Markov-modulated (MM) binomial counting process, also called a binomial counting process under regime switching. Such a process naturally appears in the context of credit risk when multiple obligors are present. Markov-modulation takes place when the failure/default rate of each individual obligor depends on an underlying Markov chain. The limit behavior under consideration occurs when the number of obligors increases unboundedly, and/or by accelerating the modulating Markov process, called rapid switching. We establish diffusion approximations, obtained by application of (semi)martingale central limit theorems. Depending on the specific circumstances, different approximations are found

Farm-level risk factors for Fasciola hepatica infection in Danish dairy cattle

Recent studies suggest that liver fluke (Fasciola hepatica) infections in cattle have increased in Denmark in recent years. This study aimed to identify potential farm level risk factors for liver fluke infection in Danish dairy farms using two different diagnostic methods. Based on liver condemnation data of all individual cattle slaughtered in Denmark, 145 and 77 farms were selected as cases and matched controls. The selection criteria were; 1) minimum 50 animals were slaughtered in 2013, 2) minimum three cases of liver condemnation due to liver flukes in 2013 (case) / no history of liver condemnation due to liver flukes for the last three years (control), and 3) control farms were located within 10 km from the case farms. Bulk tank milk (BTM) samples from the farms were analysed using enzyme-linked immunosorbent assay (ELISA), and telephone interviews were used to obtain information on the type of production, the farmers’ knowledge about liver fluke infection, grazing pattern, anthelmintic treatments and management routines. Preliminary results based on 132 case and 64 control farms indicate that grazing was significantly associated with liver fluke infection (p=0.006). However, in 12 case herds, grazing was not applied (all-in systems), suggesting indoor rearing does not completely prevent liver fluke infections, although misdiagnosis or incorrect registration at slaughter is possible. The percentage of farms allowing heifers to graze on wet areas was significantly higher in case than control farms (p<0.001). Using grazing for heifers and drinking from natural waterways were associated with liver fluke infections (p=0.07 and p=0.01). Approximately 30% of case farms tried actively to avoid infection by anthelmintic treatment or preventive management measures. The prevalences of liver flukes estimated by BTM ELISA were 75% and 12.5% for case and control groups, respectively. The negative ELISA results in some of the case herds may be due to their low in-herd prevalence, but it is still under investigation. Based on the risk analysis, we expect grazing management can be improved on many infected farms as part of the control of liver fluke. The substantial discrepancy between different diagnostic methods should be taken into account for future studies

Farm-level risk factors for Fasciola hepatica infection in Danish dairy cattle as evaluated by two diagnostic methods

The prevalence of bovine fasciolosis in Denmark is increasing but appropriate guidelines for control are currently lacking. In order to help develop a control strategy for liver fluke, a risk factor study of farm management factors was conducted and the utility of bulk tank milk (BTM ELISA) as a tool for diagnosis in Danish dairy cattle farms was assessed. This case-control study aimed to identify farm-level risk factors for fasciolosis in Danish dairy farms (&gt; 50 animals slaughtered in 2013) using two diagnostic methods: recordings of liver condemnation at slaughter, and farm-level Fasciola hepatica antibody levels in BTM. A case farm was defined as having a minimum of 3 incidents of liver condemnation due to liver fluke at slaughter (in any age group) during 2013, and control farms were located within 10 km of at least one case farm and had no history of liver condemnation due to liver fluke during 2011-2013. The selected farmers were interviewed over telephone about grazing and control practices, and BTM from these farms was collected and analysed by ELISA in 2014. The final complete dataset consisting of 131 case and 63 control farms was analysed using logistic regression. Heifers grazing on wet pastures, dry cows grazing on wet pastures, herd size, breed and concurrent beef cattle production were identified as risk factors associated with being classified as a case farm. With the categorised BTM ELISA result as the response variable, heifers grazing on wet pastures, dry cows grazing on wet pastures, and purchase of cows were identified as risk factors. Within the case and control groups, 74.8 and 12.7% of farms were positive for fasciolosis on BTM ELISA, respectively. The differences are likely to be related to the detection limit of the farm-level prevalence by the BTM ELISA test, time span between slaughter data and BTM, and the relatively low sensitivity of liver inspection at slaughter. Control of bovine fasciolosis in Denmark should target heifers and dry cows through grazing management and appropriate anthelmintic treatment, and BTM ELISA can be a useful diagnostic tool for fasciolosis in Danish dairy farms

A Diffusion-Based Analysis of a Multiclass Road Traffic Network

This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows based on conservation laws that incorporate the macroscopic fundamental diagram (a functional relationship between vehicle density and flow). Our setup is capable of handling multiple types of vehicle densities, with general macroscopic fundamental diagrams, on a network with arbitrary topology. Interpreting our system as a spatial population process, we derive, under natural scaling, fluid, and diffusion limits. More specifically, the vehicle density process can be approximated with a suitable Gaussian process, which yield accurate normal approximations to the joint (in the spatial and temporal sense) vehicle density process. The corresponding means and variances can be computed efficiently. Along the same lines, we develop an approximation to the vehicles’ travel time distribution between any given origin and destination pair. Finally, we present a series of numerical experiments that demonstrate the accuracy of the approximations and illustrate the usefulness of the results

Stability of a Stochastic Ring Network

In this paper we establish a necessary and sufficient stability condition for a stochastic ring network. Such networks naturally appear in a variety of applications within communication, computer, and road traffic systems. They typically involve multiple customer types and some form of priority structure to decide which customer receives service. These two system features tend to complicate the issue of identifying a stability condition, but we demonstrate how the ring topology can be leveraged to solve the problem