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Comparative Analysis of the Asymptotic Characteristics of Markov and Non-Markov Models of Queuing System with Two Types of Applications

Student: Daria Obedkina

Supervisor: Yulia Grishunina

Faculty: HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE)

Educational Programme: Applied Informatics (Bachelor)

Final Grade: 10

Year of Graduation: 2017

In this paper I considered M|G|2|2 non-Markov queuing system with two types of applications and various parameters of intensity of entering stream and service intensity. The purpose of this study is to clarify the correctness of using Markov model for description of non-Markov queuing system. For M|G|2|2 system I created the simulation model using open-source online service SageMathCloud, the mathematical model of queuing system in the form of a three-dimensional Markov process and the Markov model. I calculated such asymptotic characteristics as probability of losing an application and average queue length for each of these models. The values of the characteristics of Markov model turned to be very close to the values of the characteristics of simulation model and mathematical model of queuing system in the form of a three-dimensional Markov process, therefore the description of non-Markov queuing system using Markov model is correct and can be used to simplify the process of optimization of such systems. The results of this investigation can be used in any sphere related to queuing systems.

Full text (added May 25, 2017)

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