Algorithms for estimating throughput characteristics in a generalized call center model

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

doi:10.1134/s0005117916070067

Cited by 5 publications

(2 citation statements)

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“…Relationship ( 5) can be used for the estimation of the error caused by truncation of the used state space (see Appendix A), for the indirect measurement of the intensity of primary calls and for solving a variety of other problems arising in the exact and approximate analysis of the introduced model [2,[18][19][20]. To find P(i) and J(i), it is necessary to solve the system of state Equation (1).…”

Section: Basic Model Descriptionmentioning

confidence: 99%

“…It allows use of Markov processes for model description but seriously complicates the numerical analysis. Performance measures can be found by solving the system of state equations either using the Gauss-Seidel iterative algorithm [2,[18][19][20] or by matrix-geometric methods, when the corresponding Markov process has a suitable structure [17,21,22]. The first approach is time-consuming, and the last is numerically unstable for real values of input parameters because of the necessity to convert a large matrix.…”

Section: Introductionmentioning

confidence: 99%

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Estimation of the Performance Measures of a Group of Servers Taking into Account Blocking and Call Repetition before and after Server Occupation

Stepanov

2021

Mathematics

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The model of a fully available group of servers with a Poisson flow of primary calls and the possibility of losses before and after occupying a free server is considered. Additionally, a call can leave the system because of the aging of transmitted information. After each loss, there is some probability that a customer repeats the call. Such models are seen in the modeling of various telecommunication systems such as emergency information services, call and contact centers, access nodes, etc., functioning in overloading situations. The stationary behavior of the system is described by the infinite-state Markov process. It is shown that stationary characteristics of the model can be calculated with the help of an auxiliary model of the same class but without call repetitions due to losses occurring before and after the occupation of a free server and the aging of transmitted information. The performance measurements of the auxiliary model are calculated by solving a system of state equations using a recursive algorithm based on the concept of the truncation of the used state space. This approach allows significant savings of computer resources to be made by ignoring highly unlikely states in the process of calculation. The error caused by truncation is estimated. The presented numerical examples illustrate the use of the model for the elimination of the negative effects of emergency information service overload based on the filtering of the input flow of calls.

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Section: Basic Model Descriptionmentioning

confidence: 99%