| Autor: |
Alexander Dudin, Sergey Dudin, Rosanna Manzo, Luigi Rarità |
| Jazyk: |
angličtina |
| Rok vydání: |
2024 |
| Předmět: |
|
| Zdroj: |
AIMS Mathematics, Vol 9, Iss 5, Pp 12144-12169 (2024) |
| Druh dokumentu: |
article |
| ISSN: |
2473-6988 |
| DOI: |
10.3934/math.2024593?viewType=HTML |
| Popis: |
A queueing system with the discipline of flexible limited sharing of the server is considered. This discipline assumes the admission, for a simultaneous service, of only a finite number of orders, as well as the use of a reduced service rate when the bandwidth required by the admitted orders is less than the total bandwidth of the server. The orders arrive following a batch-marked Markov arrival process, which is a generalization of the well-known $ MAP $ (Markov arrival process) to the cases of heterogeneous orders and batch arrivals. The orders of different types have different preemptive priorities. The possibility of an increase or a decrease in order priority during the service is suggested to be an effective mechanism to prevent long processing orders from being pushed out of service by just-arrived higher-priority orders. Under a fixed priority scheme and a mechanism of dynamic change of the priorities, the stationary analysis of this queueing system is implemented by considering a suitable multidimensional continuous-time Markov chain with a generator that has an upper Hessenberg structure. The possibility of the optimal restriction on the number of simultaneously serviced orders is numerically demonstrated. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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