Performance Measures of Emergency Services in Case of Overload

Stepanov, S. N.; Stepanov, Mikhail S.; Shishkin, Maxim O.

doi:10.1007/978-3-030-66471-8_33

Cited by 5 publications

(11 citation statements)

References 14 publications

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“…Modern telecommunication equipment allows people to ask for assistance at any time and from almost anywhere. Technically, such types of connection are organized through public-safety answering points (PSAP) [1,2]. PSAP is the basis of public-safety systems because it allows a citizen to reach primary emergency services such as police, fire-fighting, ambulance, etc.…”

Section: Introductionmentioning

confidence: 99%

“…This problem can be solved by available planning tools based on standard queueing models. However, all emergency services are exposed to overloading situations caused by both natural (earthquakes, floods) and human (fires, terrorist attacks, nuclear accidents) factors [1,2]. The vast majority of citizens seeing or suffering the same incident try to reach emergency services almost at the same time, creating conditions for overload.…”

Section: Introductionmentioning

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%

“…Furthermore, we refer to this model as a basic model with repeated calls. Performance measures of this model can be found using a recursive algorithm based on the concept of truncation of the model's state space [2,17,19,20,23]. For this model, the asymptotic formulae for the calculation of characteristics in the case of extreme load can be also found in explicit form [24].…”

Section: Introductionmentioning

confidence: 99%

“…The closest model with retrials to the model considered in this paper was analyzed in [2,19]. That model consists of a fully available group of servers with the possibility of waiting.…”

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: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The closest model with retrials to the model considered in this paper was analyzed in [2,19]. That model consists of a fully available group of servers with the possibility of waiting.…”

Section: Introductionmentioning

confidence: 99%

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