# Queueing System Operating in Random Environment as a Model of a Cell Operation

Kim, Chesoong;Dudin, Alexander;Dudina, Olga;Kim, Jiseung

• Accepted : 2016.05.20
• Published : 2016.06.30
• 25 6

#### Abstract

We consider a multi-server queueing system without buffer and with two types of customers as a model of operation of a mobile network cell. Customers arrive at the system in the marked Markovian arrival flow. The service times of customers are exponentially distributed with parameters depending on the type of customer. A part of the available servers is reserved exclusively for service of first type customers. Customers who do not receive service upon arrival, can make repeated attempts. The system operation is influenced by random factors, leading to a change of the system parameters, including the total number of servers and the number of reserved servers. The behavior of the system is described by the multi-dimensional Markov chain. The generator of this Markov chain is constructed and the ergodicity condition is derived. Formulas for computation of the main performance measures of the system based on the stationary distribution of the Markov chain are derived. Numerical examples are presented.

#### Keywords

Multi-Server Queueing;Multi-Dimensional Markov Chain;Random Environment;Cell Operations

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#### Cited by

1. Queueing systems with correlated arrival flows and their applications to modeling telecommunication networks vol.78, pp.8, 2017, https://doi.org/10.1134/S000511791708001X

#### Acknowledgement

Supported by : National Research Foundation of Korea (NRF)