Application of Queuing Theory to Vehicular Traffic on Nakuru Total Road Stretch

 Nations strive to avoid losing revenue and human lives through long traffic snarl ups and frequent accidents on the roads. For this reason Considerations must be made to increase the number of lanes or even better to change from a single carriage to more robust dual carriages. However number of lanes and dual carriage alone serve no purpose for the accidents frequencies and traffic snarl ups that appear to defy even the most modern and sophisticated highway designs. Service time for traffic using such roads would need to be improved. Clearly therefore a numerical model is necessary for the road designers and developers to help understand road improvement demands. In this paper we establish the queue model for the Nakuru – Salgaa road Stretch and test the model with real data from the Case Study. Data is collected between the Soil- junction and the Total junction. We derive the arrival rate, service rate, utilization rate and the probability of Bulking using the M/M/1 queuing model. It is estimated that the arrival rate at the Soil- junction is 37 vehicles per minute and at total junction the service rate is 44 Vehicles per minute this does not march the dwindle service rates in section that are now black spots. The average number of vehicles on single road stretch is on average 15 per minute with some sections recording a high of 40 vehicles per minute and the utilization of the sections of stretch is on average 0.8. The benefit of performing the queue analysis for the road stretch is finally discussed and recommendations provided. 

Robust estimation of variance in the presence of nearest neighbour imputation

The problem of estimating the variance of an estimator of the population total when missing values have been filled using a Nearest Neighbour (NN) imputation method is considered. The estimator is developed assuming a more general model than those considered in earlier studies. In an empirical study involving two artificial populations, the proposed estimator is found to perform better or as well as other two estimators in the current use. African Journal of Science and Technology Vol.4(2) 2003: 5-1

GENERALISED MODEL BASED CONFIDENCE INTERVALS IN TWO STAGE CLUSTER SAMPLING

<p>Chambers and Dorfman (2002) constructed bootstrap confidence intervals in model based estimation for finite population totals assuming that auxiliary values are available throughout a target population and that the auxiliary values are independent. They also assumed that the cluster sizes are known throughout the target population. We now extend to two stage sampling in which the cluster sizes are known only for the sampled clusters, and we therefore predict the unobserved part of the population total. Jan and Elinor (2008) have done similar work, but unlike them, we use a general model, in which the auxiliary values are not necessarily independent. We demonstrate that the asymptotic properties of our proposed estimator and its coverage rates are better than those constructed under the model assisted local polynomial regression model.</p

NONPARAMETRIC MIXED RATIO ESTIMATOR FOR A FINITE POPULATION TOTAL IN STRATIFIED SAMPLING

<p>We propose a nonparametric regression approach to the estimation of a finite population total in model based frameworks in the case of stratified sampling. Similar work has been done, by Nadaraya and Watson (1964), Hansen et al (1983), and Breidt and Opsomer (2000). Our point of departure from these works is at selection of the sampling weights within every stratum, where we treat the individual strata as compact Abelian groups and demonstrate that the resulting proposed estimator is easier to compute. We also make use of mixed ratios but this time not in the contexts of simple random sampling or two stage cluster sampling, but in stratified sampling schemes, where a void still exists.</p

Adaptive Nonparametric Variance Estimation for a Ratio Estimator

Kernel estimators for smooth curves require modifications when estimating near end points of the support, both for practical and asymptotic reasons. The construction of such boundary kernels as solutions of variational problem is a difficult exercise. For estimating the error variance of a ratio estimator, we suggest an alternative estimation procedure using the theory of local linear regression. The proposed estimator adapts robustly to both interior and boundary points. We also derive the asymptotic mean square error of the new estimator and conditions under which it is efficient. Journal of Agriculture, Science and Technology Vol.3(1) 2001: 34-4

Deriving Penalized Splines For Estimation Of Time Varying Effects In Survival Data

Abstract: The major interests of survival analysis are either to compare the failure time distribution function or to assess the effects of covariate on survival via appropriate hazards regression models. Cox’s proportional hazards model (Cox, 1972) is the most widely used framework, the model assumes that the effect on the hazard function of a particular factor of interest remains unchanged throughout the observation period (Proportionality assumption). For a continuous prognostic factor the model further assumes linear effect on the log hazard function (Linearity assumption). Assumptions that many authors have found to be questionable when violated since they may result to biased results and conclusions and as such non-linear risk functions have been suggested as the suitable models.In this paper, we propose a flexible method that models dynamic effects in survival data within the Cox regression framework. The method is based on penalized splines. The model offers the chance to easily verify the presenceof PH and timevariation. We provide a detailed analysis and derivation of the penalized splines in the context of survival data

NONPARAMETRIC MIXED RATIO ESTIMATOR FOR A FINITE POPULATION TOTAL IN STRATIFIED SAMPLING

We propose a nonparametric regression approach to the estimation of a finite population total in model based frameworks in the case of stratified sampling. Similar work has been done, by Nadaraya and Watson (1964), Hansen et al (1983), and Breidt and Opsomer (2000). Our point of departure from these works is at selection of the sampling weights within every stratum, where we treat the individual strata as compact Abelian groups and demonstrate that the resulting proposed estimator is easier to compute. We also make use of mixed ratios but this time not in the contexts of simple random sampling or two stage cluster sampling, but in stratified sampling schemes, where a void still exists

GENERALISED MODEL BASED CONFIDENCE INTERVALS IN TWO STAGE CLUSTER SAMPLING

Chambers and Dorfman (2002) constructed bootstrap confidence intervals in model based estimation for finite population totals assuming that auxiliary values are available throughout a target population and that the auxiliary values are independent. They also assumed that the cluster sizes are known throughout the target population. We now extend to two stage sampling in which the cluster sizes are known only for the sampled clusters, and we therefore predict the unobserved part of the population total. Jan and Elinor (2008) have done similar work, but unlike them, we use a general model, in which the auxiliary values are not necessarily independent. We demonstrate that the asymptotic properties of our proposed estimator and its coverage rates are better than those constructed under the model assisted local polynomial regression model

Non-Parametric Estimator for a Finite Population Total Under Stratified Sampling Incorporating a Hybrid of Data Transformation and Reflection Techniques

Survey sampling methods are used in the estimation of population parameters of interest. This field has received increased demand due to the reliable statistics they produce. Information is extracted from the samples and used to make inferences about the population. In this paper, a nonparametric estimator for a finite population total that addresses the problem of boundary bias is proposed. The properties of this estimator were studied in order to determine its accuracy. The estimator was applied to a simulated data and the analysis was done using R statistical package version i386 4.0.3 and the results of the bias confirmed. The performance of the proposed estimator was tested and compared to the design-based Horvitz-Thompson estimator, the model-based approach proposed by Dorfman and the ratio estimator. This was done by studying both the unconditional and conditional properties of the estimators under the linear, quadratic and exponential mean functions. The proposed estimator outperformed other estimators in quadratic and exponential mean functions and therefore can be recommended for estimation and addressing the boundary problem. Keywords: data transformation, data reflection, boundary bia