SIMULATION

The object of this paper is to present a hybrid solution to the problem of simulating an ideal transport lag hav ing a variable time delay. The dynamic range over which the allowable time delay may be realized by this tech nique is limited on the low end by the sampling rate and execution time of the digital computer, and on the high end by the memory capacity of the digital computer. Experimental results using signals consisting of either sinusoidal waveforms or random noise are presented.

A new classification of Monte Carlo digital computer simulations is suggested.

The body of this paper centers on the determination of sample sizes and confidence intervals associated with a simulation model which has a multinomially distributed output.

A brief description of a 'multinomial' Monte Carlo model is given. The theoretical considerations put forth are then verified on this model.

Systems philosophy provides the theoretical framework linking diverse applications of computer simulation. Natural systems and man-made systems may be regarded as end members of a spectrum of system types. Simula tion of man-made systems employs operations research techniques; the objectives of simulation are to optimize system design and to test the performance of models under differing parameter settings. Simulation of natural systems cannot readily utilize specialized simulation lan guages, as these are designed primarily for industrial and business applications. The objectives of simulating natu ral systems are normally to test alternative models and to see how they react under various conditions; the natural system itself cannot be changed (unless it is partly man- influenced)-only the model can.

This paper is a brief report on an investigation into the performance of integration routines used in the simula tion of dynamic systems by general-purpose digital simu lation programs. The performance is compared with respect to overall speed, accuracy, and convenience. Several routines are considered, including rectangular, Runge-Kutta, Runge-Kutta-Blum, Runge-Kutta-Mer son, and Adams-Moulton methods. The last two may use either fixed- or variable-step-size methods. The Tus tin method and the State-Transition method are also included.

By examining the performance of the routines through tests on representative systems, it is shown that for the simulation of linear systems the state transition method works best. For the general simulation of linear and non linear systems the variable-step-size Runge-Kutta-Mer son method proves to be most accurate and most efficient. The variable-step-size method may be designed to gen erate outputs at uniform intervals, thus greatly enhanc ing its value when synchronous interaction with other parts of a simulation is required.

The rotational acceleration for a rigid body has traditionally been represented by three simultaneous equations. Be cause of the computation time required for the iterative solution of simultaneous equations using a digital com puter, it is desirable to transform these equations to an explicit form for digital solution. The rotational equations are linear in the acceleration components. Thus, an explicit form can be obtained by either a determinate or a substi tution method. For problems where solution requires two or more of the cross-products-of-inertia terms, the determ inate method yields the most efficient equation form for digital solution. For the special case of body-plane sym metry (i.e., two cross-products-of-inertia terms are neg lected), the substitution method yields the most efficient form.