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THE ANALYSIS OF CALL CENTER MODEL IN CASE OF OVERLOAD
Sergey N. Stepanov, MTUCI, Moscow, Russia, stpnvsrg@gmail.com
Maxim O. Shishkin, MTUCI, Moscow, Russia, mackschischkin1@yandex.ru
Georgiy. K. Sosnovikov, MTUCI, Moscow, Russia, sosnovikov.georgy@yandex.ru
Mikhail S. Stepanov, MTUCI, Moscow, Russia, mihstep@yandex.ru
Leonid A. Vorobeychikov, MTUCI, Moscow, Russia, voroleonid@yandex.ru
Hanna M. Zhurko, MTUCI, Moscow, Russia, hazhurko@gmail.com
Abstract
The mathematical model of call center functioning is constructed and analyzed. In the model multi-skilled routing based on usage of one group of operators for simple requests and two groups of experts (consultants) handling more advanced topics is taken into account. Call center model is considered in case of overload. It means that large portion of coming requests are repeated requests caused by insufficient amount of operators, consultants or waiting positions. In case of blocking or unsuccessful waiting time a subscriber with some probability can repeat a call. Primary and repeated requests for servicing are coming after exponentially distributed time intervals. Customer service time maximally consist of three phases: listening the recorded message from the IVR, receiving the information of general character from an operator, and getting specialized information from a consultant of the chosen group. It is supposed that all random variables used for the model description have exponential distribution and are independent from each other. Markov process that describes model functioning is constructed. The definitions of main performance measures are formulated through values of probabilities of model’s stationary states. Algorithm of performance measures estimation is suggested based on solving the system of state equations by Gauss-Zeidel iterative algorithm. Expressions that relates introduced performance measures in form of conservation laws are derived. It is shown how to use found relations for indirect measurement of the intensity of primary requests and other characteristics of call center functioning. Numerical examples are presented.
Keywords: call-center, system of state equations, performance evaluation, multi-skilled routing, repeated attempts.
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Information about authors:
Sergey N. Stepanov, 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 of multimedia networks and communication services, Moscow, Russia
Georgiy K. Sosnovikov, docent, Cand. Tech. Sciences, MTUCI, the chair of informatics, Moscow, Russia
Mikhail S. Stepanov, docent, Cand. Tech. Sciences, MTUCI, the chair of communication networks and commutation systems, Moscow, Russia
Leonid A. Vorobeychikov, docent, Cand. Tech. Sciences, MTUCI, the chair of informatics, Moscow, Russia
Hanna M. Zhurko, PhD student, MTUCI, the chair of communication networks and commutation systems, Moscow, Russia