THE TRANSIENT SOLUTION FOR M/G/1 QUEUEWITH SERVER VACATIONS

In this paper, the transient solutions for M/G/1 queues with single server vacation and multiple server vacations are firstly studied, and the recursion expressions of their Laplace transform are given. Further the distribution and stochastic decomposition result of the queue length at a random point in equilibrium are directly obtained from the transient solution. As will be seen this paper provides a intuitive and elegant method for studying transient solutions for M/G/1 queues with single server.

LONG-TIME BEHAVIOR OF TRANSIENT SOLUTIONS FOR CELLULAR NEURAL NETWORK SYSTEMS

By establishing concept an transient solutions of general nonlinear systems converging to its equilibrium set, long-time behavior of solutions for cellular neural network systems is studied. A stability condition in generalized sense is obtained. This result reported has an important guide to concrete neural network designs.

Analytical solution for a circular roadway considering the transient effect of excavation unloading

The rocks surrounding a roadway exhibit some special and complex phenomena with increasing depth of excavation in underground engineering.Quasi-static analysis cannot adequately explain these engineering problems.The computational model of a circular roadway considering the transient effect of excavation unloading is established for these problems.The time factor makes the solution of the problem difficult.Thus,the computational model is divided into a dynamic model and a static model.The Laplace integral transform and inverse transform are performed to solve the dynamic model and elasticity theory is used to analyze the static model.The results from an example show that circumferential stress increases and radial stress decreases with time.The stress difference becomes large gradually in this progress.The displacement increases with unloading time and decreases with the radial depth of surrounding rocks.It can be seen that the development trend of unloading and displacement is similar by comparing their rates.Finally,the results of ANSYS are used to verify the analytical solution.The contrast indicates that the laws of the two methods are basically in agreement.Thus,the analysis can provide a reference for further study.

Analysis of the Flow of a Molten Slag in an Open Channel Using Transient and Steady-State Solutions of the Saint-Venant Equations

In recent years, metallurgical slags have been increasingly used as materials for the manufacture of cement, pavement and filling material. The transport of the molten slag to the receiving pots is carried out through open channels. The transient and steady-state flow of a molten slag in a rectangular open channel is numerically analyzed here. For the transient flow, the Saint-Venant equations were numerically solved. For the steady-state flow, the derivatives in time and space in the Saint-Venant equations were set equal to zero and a polynomial of degree 3 is obtained whose roots are the slag height values. It was assumed that the viscosity of the slag has an Arrhenius-type behavior with temperature. Four values of temperature values, namely 1723.15, 1773.15, 1823.15, 18873.15 ˚K, and five values of the angle of inclination of the channel, namely 1, 2, 3, 4, 5 degrees, are considered. Numerical results show that the steady-state values of the height and velocity of the molten slag depend strongly on the temperature of the slag and the angle of inclination of the channel. As the slag temperature and channel angle increase, the value of the steady-state slag height decreases. The value of the steady-state slag velocity increases as the slag temperature and channel inclination angle increase.

Research on two-step throttle characteristics of double-rotation valve port for hydraulic servo joint

The hydraulic robot with large output torque is widely used in industry,however,its precision is not high.In order to solve this problem,this paper presents a new structure of rotary valve with double-rotation valve port,which can improve the two-step throttle characteristics of the valve port,reduce the cavitation phenomenon of the valve port,and increase the output accuracy of the hydraulic servo joint.Firstly,the internal flow field of the rotary valve is simulated by using the sliding grid technology of FLUENT software,and the changing rule of the throttle position in the working process of the structure is analyzed.Secondly,compared with the simulation results of rotary valve with single-rotation valve port,it is shown that the two-step throttle characteristics of the structure are less affected by the change of the opening of the rotary valve,and the cavitation index of the joint valve port is reduced.Finally,the influence of the rotation speed of the valve core,oil supply pressure and key dimension of valve core on throttle characteristics of rotary valve have been analyzed.

Machine Interference Problem with Reliable Server under Single Vacation

The machine interference problem with reliable server under single vacation is considered here. There are M similar machines that are subject to fail or breaks down with a single server who is responsible for repairing or maintaining the failed machines. The machine fails completely at random with rate 2 and they are serviced in order of breaks down. More so, the machines operate independently but are subject to fail or break down. The service time distributions of the failed machines are assumed to be exponentially distributed with state dependent service rate #n, where n is the number of failed machines. By state dependent service rate we mean a situation where the rate of service depends on the number of failed machines present in the system. The Chapman-Kolmogorov differential equations obtained for the reliable server under single vacation model is solved through ODE45 （Runge-Kutta algorithm of order 4 and 5） in MATLAB programming language. The transient probabilities obtained are used to compute the operational measures of performance for the systems. The following time dependent operational measures of performance for the system are obtained： expected number of failed machines, expected number of operating machines, machine availability, expected idle period, expected busy period, operational utilization of the machine, the variance of the expected number of failed machine and variance of expected number of operating machine in the system. The effects of failure rate of machines, service rate of failed machines and the number of operating machines are investigated; it is observe that the rate at which machine fails and is serviced, affect the expected number of failed and operating machines in the system. The CPU time for obtaining the transient results for the systems and the variance of the systems are reported in this work.