Analysis of a Retrial Queue with Limited Processor Sharing Operating in the Random Environment
- 762 Downloads
Queueing system with limited processor sharing, which operates in the Markovian random environment, is considered. Parameters of the system (pattern of the arrival rate, capacity of the server, i.e., the number of customers than can share the server simultaneously, the service intensity, the impatience rate, etc.) depend on the state of the random environment. Customers arriving when the server capacity is exhausted join orbit and retry for service later. The stationary distribution of the system states (including the number of customers in orbit and in service) is computed and expressions for the key performance measures of the system are derived. Numerical example illustrates possibility of optimal adjustment of the server capacity to the state of the random environment.
KeywordsProcessor sharing Markovian arrival process Random environment
The publication was financially supported by the Ministry of Education and Science of the Russian Federation (the Agreement number 02.a03.21.0008) and by the Belarusian Republican Foundation for Fundamental Research (grant F16MV-003).
- 1.Samouylov, K., Naumov, V., Sopin, E., Gudkova, I., Shorgin, S.: Sojourn time analysis for processor sharing loss system with unreliable server. In: Wittevrongel, S., Phung-Duc, T. (eds.) ASMTA 2016. LNCS, vol. 9845, pp. 284–297. Springer, Cham (2016). doi: 10.1007/978-3-319-43904-4_20 CrossRefGoogle Scholar
- 2.Samouylov, K., Sopin, E., Gudkova, I.: Sojourn time analysis for processor sharing loss queuing system with service interruptions and MAP arrivals. In: Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (eds.) DCCN 2016. CCIS, vol. 678, pp. 406–417. Springer, Cham (2016). doi: 10.1007/978-3-319-51917-3_36 CrossRefGoogle Scholar