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THE CONSTRUCTION AND ANALYSIS OF CALL-CENTER MODEL IN OVERLOAD TRAFFIC CONDITION
DOI: 10.36724/2072-8735-2020-14-7-42-50
Sergey N. Stepanov, MTUCI, Moscow, Russia, stpnvsrg@gmail.com
Maxim O. Shishkin, MTUCI, Moscow, Russia, mackschischkin1@yandex.ru
Mikhail S. Stepanov, MTUCI, Moscow, Russia, mihstep@yandex.ru
Hanna M. Zhurko, MTUCI, Moscow, Russia, hazhurko@gmail.com
Abstract
The functional and mathematical models of call center working in case of overload are constructed and analyzed. In the model the following features are considered: the possibility of serving of coming request by IVR (Interactive Voice Response); the option of waiting the beginning of service in case of blocking and the opportunity of request repetition in case of occupation of all waiting positions or unsuccessful finishing of waiting time. Markov process that describes model functioning is defined. Main performance measures of requests coming and serving are given with help of values of stationary probabilities of model’s states. The values of performance measures are found after solving the system of state equations by Gauss-Zeidel iterative approach. Expressions that relates the model’s main performance measures in form of local and global conservation laws are found. The obtained results can be used for indirect measurement of intensity of primary requests and the probability of call repetition. It is shown how to use the model and the derived results for reducing the negative effects of overload by filtering the input flows of primary and repeated attempts. The usage of the model for calculation of the numbers of operators and waiting places required to serve the incoming traffic flows with given value of probability of call losses and mean value of waiting the beginning of service is considered. Numerical results that illustrate the implementation of the derived expressions and algorithms are given.
Keywords: call center, Markov process, system of state equations, performance measures, overload..
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Information about authors:
Stepanov Sergey, professor, doctor of science, MTUCI, head of the chair of communication networks and commutation systems, Moscow, Russia
Maxim O. Shishkin, graduate student, MTUCI, the chair of multimedia networks and communication services, Moscow, Russia
Mikhail S. Stepanov, docent, Cand. Tech. Sciences, MTUCI, the chair of communication networks and commutation systems, Moscow, Russia
Hanna M. Zhurko, PhD student, MTUCI, the chair of communication networks and commutation systems, Moscow, Russia