Generally, server utilization must be less than 1 for a queueing system to be stable. One exception that maintains stability with server utilization equal to 1, is the D/D/1 case with identical interarrival times and service times. In this paper, we present several other models which are stable with server utilization equal to 1.

A watered-down version of the cutting stock algorithm has existed for a few centuries before the industrial revolution but no real formulation or solution to the problem was known other than for a few heuristic algorithms used under specific cases pertaining to the logging industry. The first formulations and solutions of the cutting stock problem was published about 6 decades ago by Gilmore and Gomory in the Operation research journal [1]. In that, they have explained the concept by using crude optimization techniques which are not applicable to most conditions found in the contemporary business environment. Our research project involves cut-ting wooden sheets and wooden rods of specific dimensions based on the requirements of the customers of Moratuwa Timber Work (MTW). The main focus of this paper is to find the optimal cutting patterns by minimizing the wastage and the trim loss. This is achieved with the aid of a web enabled database, using Java codes and Lingo programs.

This paper is concerned with the construction of two-step hybrid block Simpson’s method with four off-grid points for the solutions of stiff systems of ordinary differential equations (ODEs). This is achieved by transforming a k-step multi-step method into continuous form and evaluating at various grid points to obtain the discrete schemes. The discrete schemes are applied as a block for simultaneous integration. The block matrix equation is A-stable and of order [7, 7, 7, 7, 7, 7]T. This order ‘p’ is achieved by the aid of Maple13 software program. The performance of the method is demonstrated on some numerical experiments. The results revealed that the hybrid block Simpson’s method is efficient, accurate and convergent on stiff problems.

In this paper, we propose an implicit two-step third derivative hybrid block method with one off-step point for the direct solution of second order Ordinary Differential Equations. We adopted the method of interpolation and collocation of power series approximate solution to generate the continuous hybrid linear multistep method, which was evaluated at non-interpolated step points to give a continuous block method. The discrete block method was recovered when the continuous block method was evaluated at all step points. The basic properties of the method were investigated and the method was found to be zero-stable, consistent and convergent. The efficiency of the method was tested on some stiff equations and was found to give better approximation than the existing methods with which we compared our results.

Forced convective heat transfer in parallel microchannels with asymmetric and symmetric wall thermal conditions under hydrodynamically and thermally fully developed flow is investigated using control volume technique for steady, two dimensional flow. Incompressible Navier-Stokes and energy equations are solved applying velocity slip and temperature jump boundary conditions on the walls. Simulations are validated comparing with the experimental results available in the literature. Simulations are performed for different temperature difference between the walls and the gas as well as the inlet velocity and ambient pressure conditions. Either the wall heating or wall cooling cases are examined taking Nitrogen gas as the working fluid. The influences of Knudsen number, Reynolds number and temperature difference on Nusselt number are observed. It is shown here that for asymmetric wall thermal condition for temperature dependent thermal conductivity the Nusselt number is lower for higher temperature difference where as for symmetric wall thermal condition Nusselt number is higher for higher temperature difference.

In this work, we present an alternative method, namely, Graph Contraction Technique for solving the transportation problem which is a special class of Linear Programming Problem. We represented the transportation problem as a bipartite graph and solved it iteratively. To illustrate the method, two numerical examples are solved and the obtained solutions are compared with those obtained via Vogel approximation method. The present method yields the same initial basic feasible solutions of the problem. However, the present method is found to be very easy to understand; use and implement compared to the Vogel approximation method and can be applied on real life transportation problems by the decision makers.

A one-step hybrid block method for initial value problems of general second order Ordinary Differential Equations has been studied in this paper. In the derivation of the method, power series is adopted as basis function to obtain the main continuous scheme through collocation and interpolations approach. Taylor method is also used together with new method to generate the non-overlapping numerical results. The new method is then applied to solve the system of second-order stiff ordinary differential equations and the accuracy is better when compared with the existing methods in terms of error.

Evaporation is one of the climatic/meteorological factors influenced by causes of climate change. Interest in the topic of climate change has been growing over the last three decades. The threat it poses cannot be overemphasized particularly in developing economies largely due to the connection it has with national development issues. We present a regression tree grown using recursive binary splitting, cost complexity pruning and boosting to study the relationship between evaporation piche and other climatic factors such as relative humidity, solar radiation, sunshine hours, wind speed, temperature and rainfall over the city of Ilorin in Nigeria. These factors are generally seen to change with rising climatic changes in a place. Analysis of the fitted tree reveals that relative humidity, temperature and rainfall are the most important meteorological factors affecting the level of evaporation piche in the city of Ilorin.

In this study, a new one step continuous hybrid constant block method is developed using interpolation and collocation of power series approximate solution to solve initial -value problems involving third -order ordinary differential equations. The one step block method was augmented by the introduction of off grid points so as to circumvent Dahquist zero stability barrier. The block method is then applied to obtain the solution of two numerical examples for demonstration of the efficiency of the new method. The results are compared with the existing ones in literature and it is concluded that results of Continuous Hybrid Constant Block Method is more accurate than when it was implemented in predictor corrector mode or using implicit Runge-Kutta method.

The aim of this study is to examine the effects of outliers on the specification and efficiency of heteroscedastic models fitted to the daily closing share price returns series of two outstanding banks in Nigeria from January 3, 2006 to November 24, 2016. The series consists of 2690 observations for each bank. The data were obtained from the Nigerian Stock Exchange. GARCH(2,0) model with respect to student-t error distribution and GARCH(1,1) model under normal error distribution were successfully fitted to the outlier contaminated series of Diamond bank and United bank for Africa accordingly. On the contrary, EGARCH(1,1) model with respect to student-t error distribution adequately captured the changing variance in the outlier adjusted series of the two banks considered. Substantial evidence revealed that the presence of outliers in returns series leads to model misspecification and adjusting for such outliers ensures model efficiency.

We construct an ordinary differential equation representation of an impulsive system by a bijective transformation that structurally maps the solutions of the initial value problem of the impulsive differential equations to the solutions of the initial value problems of the ordinary differential equations. Established in this work is the relationship between impulsive differential equations and ordinary differential equations which play a fundamental role in qualitative analysis of the former. It is also established that an n-dimensional impulsive differential equation can be represented in terms of a 2n-dimensional ordinary differential equation. Figures are used to demonstrate the practicability of the methodology developed.

Designing an appropriate central composite design involves selection of the right type of central composite design. The various Central composite designs(CCDs); Spherical central composite design (SCCD), Rotatable central composite design (RCCD), Orthogonal central composite design (OCCD) and Face centered cube design (FCCD) were compared for factors k =2 to 6 using the D, G and A criteria. The a (axial) values were obtained for the various Central composite design (SCCD, RCCD, OCCD and FCD) and the values used to find relevant results for factors k=2 to 6. The efficiency values were obtained for the D, A and G optimality criteria in which larger values imply better design. The axial portion and cube portion were replicated with the center points increased one and three times. The results show that replicating the star points tends to reduce the D and G-optimality criteria of the CCDs (SCCD, RCCD, OCCD and FCCD) at some factor levels while it is different for the A optimality criterion. The results suggest replication affects the different criteria in very different ways because what improves one criterion may be detrimental to a different criterion. The overall results show that G optimality criteria performed better than D and A optimality in different factor levels and replications.

In this paper, we consider a prey-predator fishery model in a three –patch aquatic habitat with selective harvesting of predator and prey populations. We attempt to study the qualitative behaviour of stability and co-existence steady state solution in an interaction between prey and predator populations due to variation of the harvesting effort when other model parameters are fixed using the method of numerical simulation. The innovation of this simulation technique has been used to determine the fraction of harvest and un-harvest resource biomass for prey and predator populations. Explicit expressions and values of the maximum sustainable yield (MSY) and the corresponding populations’ level are obtained. Some sort of control is suggested to avoid over exploitation of resource biomass. Graphical solutions of the model are provided.

In this paper, we develop a vector error correction model for US natural gas market. It allows us to analyze the linkage effect of the natural gas price from 1998 to 2016. In particular, we prove the evidence that there is a long-term equilibrium relationship in US natural gas, coal and crude oil prices. Impulse response function and variance decomposition are used to examine the linkage effects that a shock in coal and crude oil price would have on natural gas price.

In this paper, we based on 7 multi index comprehensive evaluation methods, a system of selecting multi-index comprehensive evaluation method is put forward and combined with the multi-index data of air quality in four cities a day, the flow of the multi-index evaluation method proposed above is analyzed, which shows the feasibility of the system and reduces the blindness in the selection of multi-index comprehensive evaluation methods.