**MASS SERVICE THEORY** (synonym *theory of turns*) — set mathematical (analytical and machine) methods of a research of the systems of mass service directed to development of optimal variants of management by them. In medicine and health care methods M. of the lake of t. apply at problem solving of the organization of medical aid, at a research of processes of distribution of epidemics, studying of demographic processes and in other cases when the solution of the corresponding task is connected with processing of big arrays of information (flows of the requirements) arriving from bodies of interest (systems). Can be examples of systems of mass service: the hospital servicing the arriving flow of sick (requirements); the service of emergency medical service designed to service a flow of calls (requirements) arriving on control office of this service; any directory service which is carrying out search and submission of necessary information to clients etc.

Systems of mass service represent a uniform complex of the arriving flows of requirements, the servicing devices or devices, and also «turns» of the requirements expecting service. According to it at a task of any system of mass service it is necessary to define: patterns of formation of the entering flows of the requirements considering in addition to the moments of receipt of requirements, also various signs characterizing these requirements; the rules regulating process of formation of turns — i.e. discipline of turn (these rules can depend on the signs characterizing requirements and on timepoint of receipt them in system); the rules regulating an order of service of the requirements arriving or standing in a queue, their attachment to the servicing devices and probabilistic and time characteristics of direct service (i.e. discipline of service).

The recommendations about character and quality of their functioning which are usually coming down to appointment or reassignment of any signs of requirements, change of discipline of turns, service etc. are result of the analysis of systems of mass service.

Distinctiveness of systems of mass service is that accidental mechanisms play a major role in formation of process of functioning of such systems. Therefore M. of the lake of t. is based on such mathematical disciplines as probabilities theory (see) and theory of accidental processes. For the applied purposes the method of statistical modeling on the COMPUTER consisting in program imitation of all complex of the mechanisms setting dynamics of the modelled system of mass service is used generally. For assessment of parameters and indicators of quality of the studied models methods of mathematical statistics are used.

M of the lake of t. investigates various systems, sometimes radically differing from each other. In particular, can be them: systems with expectation when the arriving requirements can expect the beginning of service (shop, informatsionnospravochny service); systems with limited expectation when restrictions for an allowed time of expectation (-tsa, ambulance) etc. are imposed. According to it apply various, sometimes excluding combined use, indicators to evaluation test of functioning of system of mass service: probabilistic characteristics (distributions, average etc.) lengths of turns, dlitelnost of expectation, number of the requirements which did not receive service, total lost time of system etc.

See also Mathematical methods (in medicine) .

**Bibliography:** Buslenko N. P. Modeling of complex systems, M., 1978, bibliogr.; Gnedenko B. V. and Kovalenko I. N. Introduction to the theory of mass service, M., 1966, bibliogr.; Klimov G. P. Stochastic systems of service, M., 1968, bibliogr.; P about-zenberg V. Ya. and P r about x about r about in A. I. What is the theory of mass service, M., 1965, bibliogr.; With and and t and T. L. Elements of the theory of mass service and its appendix, the lane with English, M., 1965, bibliogr.; Hinchin A. Ya. Works on the mathematical theory of mass service, M., 1963.

*V. V. Kalashnikov.*