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Mathematical Model of Call Center in the Form of Multi-Server Queueing System
- Source :
- Mathematics. 2021. Vol. 9, № 22. P. 2877 (1-13), Mathematics, Vol 9, Iss 2877, p 2877 (2021), Mathematics, Volume 9, Issue 22
- Publication Year :
- 2021
- Publisher :
- MDPI AG, 2021.
-
Abstract
- 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.
- Subjects :
- Service (business)
Mathematical optimization
Stationary distribution
Optimization problem
Mathematical model
Computer science
General Mathematics
matrix-geometric method
Function (mathematics)
Poisson distribution
multi-server queue
symbols.namesake
Hyperexponential distribution
hyperexponential approximation
системы массового обслуживания
QA1-939
Computer Science (miscellaneous)
Matrix geometric method
symbols
матрично-геометрический метод
hyperexponential service
многосерверные системы
Engineering (miscellaneous)
Mathematics
Subjects
Details
- ISSN :
- 22277390
- Volume :
- 9
- Database :
- OpenAIRE
- Journal :
- Mathematics
- Accession number :
- edsair.doi.dedup.....a76c2b67dc6e284557c9a986ec245ccd