Construction and analysis of a generalized contact center model

Stepanov, S. N.; Stepanov, Mikhail S.

doi:10.1134/s0005117914110046

Cited by 7 publications

(2 citation statements)

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“…and vector P = P(0) to separate it from other components of the solution. Then, we can rewrite (5) in the matrix form:…”

Section: The First Stage: Matrix-geometric Methodsmentioning

confidence: 99%

“…An excellent description of call centers and general issues in applying queueing models to studies were presented in [1]; some other general issues on the topic may be found in [2][3][4][5]. In this paper, we consider a call center model in the form of a multi-server queue with an incoming Poisson flow of calls, recurrent service, and an unlimited number of waiting places (M/G/N).…”

Section: Introductionmentioning

confidence: 99%

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Mathematical Model of Call Center in the Form of Multi-Server Queueing System

2021

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The paper considers the model of a call center in the form of a multi-server queueing system with Poisson arrivals and an unlimited waiting area. In the model under consideration, incoming calls do not differ in terms of service conditions, requested service, and interarrival periods. It is assumed that an incoming call can use any free server and they are all identical in terms of capabilities and quality. The goal problem is to find the stationary distribution of the number of calls in the system for an arbitrary recurrent service. This will allow us to evaluate the performance measures of such systems and solve various optimization problems for them. Considering models with non-exponential service times provides solutions for a wide class of mathematical models, making the results more adequate for real call centers. The solution is based on the approximation of the given distribution function of the service time by the hyperexponential distribution function. Therefore, first, the problem of studying a system with hyperexponential service is solved using the matrix-geometric method. Further, on the basis of this result, an approximation of the stationary distribution of the number of calls in a multi-server system with an arbitrary distribution function of the service time is constructed. Various issues in the application of this approximation are considered, and its accuracy is analyzed based on comparison with the known analytical result for a particular case, as well as with the results of the simulation.

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“…and vector P = P(0) to separate it from other components of the solution. Then, we can rewrite (5) in the matrix form:…”

Section: The First Stage: Matrix-geometric Methodsmentioning

confidence: 99%