Correlated queues with service times depending on inter-arrival times

Dai, Weimin; Hu, Jian-Qiang

doi:10.1007/s11134-021-09718-7

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Literature Review Of Queues With Interdependence In Arrival ...1

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2023

2024

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Cited by 5 publications

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“…Krishnamoorthy et al [11] examined a queueing system with finite Markov-dependent arrival and service batch sizes, and additionally considered correlated successive inter-arrival and service time durations. Dai et al [12] investigated a unique category of correlated queue in which the service duration of an arriving customer hinges upon the inter-arrival time separating them from the previous customer.…”

Section: Literature Review Of Queues With Interdependence In Arrival ...mentioning

confidence: 99%

A Two-Server Queue with Interdependence between Arrival and Service Processes

Krishnamoorthy,

Kozyrev

2023

Mathematics

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In this paper, we analyse a queueing system with two servers where the arrival and service processes are interdependent. The evolution of these processes is governed by transitions on the product space of three Markov chains, which are descriptors of the arrival and service processes. The transitions in this Markov chain follow a semi-Markov rule and the exponential distribution governs the sojourn times in the states. The stability condition of the system is derived and the stationary distribution is calculated for the system in equilibrium. Several important performance measures are provided, and numerical illustrations of the model are presented.

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Section: Literature Review Of Queues With Interdependence In Arrival ...mentioning

confidence: 99%