On the law of the iterated logarithm in hybrid multiphase queueing systems

The model of a Hybrid Multi-phase Queueing System (HMQS) under conditions of heavy traffic is developed in this paper. This is a mathematical model to measure the performance of complex computer networks working under conditions of heavy traffic. Two probability limit theorems (Laws of the iterated logarithm, LIL) are presented for a queue length of jobs in HMQS.

Application of methods of the theory of multiphase queueing systems to the problems of optimizing the resources of service companies in the field of housing sector

The scientific - methodological approach to calculation of duration and estimation of complexity of the expertise of technical and operational documentation for measuring equipment and technical devices used in the field of construction and housing sector is suggested. The approach is based on both the theory of queueing systems and probabilistic and statistical methods. The developed approach is implemented in the form of package of applied programs. The software based on complex using the principle of decomposition of object into constituent parts, the queuing theory and the method of expert estimations. The software allows on the basis of the results of statistical data processing for the past periods of work to receive both estimates of the average time of the expertise as a whole, and the estimates of the individual expertise stages. The algorithm for calculating the required number of employees for quality customer service is developed, taking into account the restriction on the waiting time of the request in the queue. The obtained results make it possible to make optimal use of working personnel at various work sites, taking into account their qualifications and training. The developed approach can be used to form a “fair price list” for private clients and enterprises - customers of expertise.

Optimal resource allocation of the servicing companies in the field of housing and public utilities on the basis of the theory of multiphase queueing systems

The mathematical model describing technological process of functioning of the servicing companies in the sphere of housing sector and communal services is offered. The model allows you to manage the resources of serving companies in the housing sector in order to improve the quality of service. The problem statement and the solution of a problem of rational distribution of resources of the service company on the example of functioning of the center of maintenance of the measuring equipment used in the sphere of housing and communal services is given. The service center is modeled as a multiphase queueing system, which includes single-phase Queuing systems with limited and unlimited queue length. Used in the paper a method of sequential linearization allows to solve tasks of control production capacity of multiphase queueing systems for the simplest incoming flows with exponential service of requirements and free streams of requirements that are describing by means of simulation modeling methods. The software was developed. The results of applying the method of consistent linearization and corresponding software to the problem of optimal redistribution of production capacity of the center for maintenance of measuring equipment used in the sphere of housing and communal services are presented.

Python for Scientific Computing Education: Modeling of Queueing Systems

In this paper, we present the methodology for the introduction to scientific computing based on model-centered learning. We propose multiphase queueing systems as a basis for learning objects. We use Python and parallel programming for implementing the models and present the computer code and results of stochastic simulations.