Example of mathematical modelling is the imitation of process of patients servicing that is used at planning of organizational actions, in particular, for the calculation of necessary resource provision at set quality of health services. Imitating modelling finds its application also at designing of the integrated information systems of hospitals.

The imitating model of process of service is based on the mathematical theory of mass servicing. Any system of mass servicing includes the following elements: an entering stream of applications for service; the turn arising when arriving applications cannot be satisfied immediately (the length of turn and a waiting time which depend on so-called discipline of service); servers on organization of which depends not only the time necessary on service of one application, but also length of turns (waiting time); a output stream of the served applications (this element appears important when the output stream of applications is entering for other system of mass servicing, for example the part of served patients in admission-diagnostic department (ADD) of a hospital is directed in emergency surgical block.

Above-mentioned abstract conceptions of the mathematical theory are convenient for modelling the process of service of patients’ entrance stream in ADD, having for an object the improvement of its temporal characteristics. Servicing systems in this case are elements of resource provision in ADD: the equipment, rooms and staff.

Entering in ADD of hospitals streams of patients are sectioned on account of appeals (symptoms and nosologies). According to these divisions the strategy of rendering of an emergency medical care is chosen, the resources necessary for service, and priorities in turns on use of each separate resource are determined. At designing of optimum model of the ADD functioning it is necessary to minimize amount of diverse streams, taking at the same time into consideration requirements of medical specifications and standards on service.

Prominent aspect of the ADD activity is multiphase nature of service of patients stream (process of service of a stream should coordinate set of the processes of receipt of applications on service initially not connected among themselves). It hinders reception of analytical decisions by methods of the theory of mass service. The only accessible instrument for reception of decisions on optimization of ADD work is an imitating modelling on a computer.

Basic advantage of use of imitating modelling in medical-organizational researches consists in that the availability of adequate models helps to avoid noneffective actions, to reduce risk of economic losses at introduction of new tactics of health services of all patients entering to a hospital.

In the models constructed on a method of analogy, processes in a nature and in model have different physical nature, but are described by the identical equations. Conditions of similarity are revealed by the analysis of dimension of physical magnitude or the analysis of the equations.

Physical models can be considered as a special case of models on the basis of analogy, when the physical nature of process in model and in a nature is the same. In connection with a generality of the physical nature it is obviously possible to research keeping similarity conditions on physical model of processes which mathematical description with necessary accuracy is not known.

Example of physical model is the complex of independent microsurgical ophthalmologic biosimulators forming uniform educational operation room and a complex of functional - apparatus ophthalmic simulators of nonsurgical structure created at the Crimean republican center of vision rehabilitation.

All types of models listed above find application in medical simulators.

The analog and physical modelling underlies the theory of similarity which bases were grounded by Newton. The big role in creation of this theory played works of M.V. Kirpichev, M.A. Mikheyev, A.A. Guhman, etc. The Theory of similarity gives rules with which help identity of course of processes in a nature and in model is provided. At that it is found out, how it is necessary to choose parameters of model. Some of them can be chosen freely proceeding from conditions of the most rational realization of simulators; others are determined from conditions of similarity as consequence of a choice of the first. In the process of training on simulators the great importance has comprehension of memory management processes.