On a Two-Server Queue with Consultation in Random Environment

Krishnamoorthy, A.; Thekkiniyedath, Resmi; Lakshmy, Balakrishna

doi:10.1007/978-3-030-33388-1_18

Cited by 1 publication

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“…Extensive illustrative numerical examples to bring out the qualitative nature of the model are presented. In [19], the model with N = 1 servers and M = 1 assistants is analyzed. All parameters of the system depend on the state of a finite state random environment.…”

Section: Introductionmentioning

confidence: 99%

Self-Service System with Rating Dependent Arrivals

et al. 2022

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A multi-server infinite buffer queueing system with additional servers (assistants) providing help to the main servers when they encounter problems is considered as the model of real-world systems with customers’ self-service. Such systems are widely used in many areas of human activity. An arrival flow is assumed to be the novel essential generalization of the known Markov Arrival Process (MAP) to the case of the dynamic dependence of the parameters of the MAP on the rating of the system. The rating is the process defined at any moment by the quality of service of previously arrived customers. The possibilities of a customers immediate departure from the system at the entrance to the system and the buffer due to impatience are taken into account. The system is analyzed via the use of the results for multi-dimensional Markov chains with level-dependent behavior. The transparent stability condition is derived, as well as the expressions for the key performance indicators of the system in terms of the stationary probabilities of the Markov chain. Numerical results are provided.

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Section: Introductionmentioning

confidence: 99%