Analysis of the GI/M/3/K queueing system by Semi-Markov process
PAMUKKALE UNIVERSITY JOURNAL OF ENGINEERING SCIENCES-PAMUKKALE UNIVERSITESI MUHENDISLIK BILIMLERI DERGISI, cilt.26, sa.1, ss.195-202, 2020 (ESCI, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 26 Sayı: 1
- Basım Tarihi: 2020
- Doi Numarası: 10.5505/pajes.2019.36974
- Dergi Adı: PAMUKKALE UNIVERSITY JOURNAL OF ENGINEERING SCIENCES-PAMUKKALE UNIVERSITESI MUHENDISLIK BILIMLERI DERGISI
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.195-202
- Anahtar Kelimeler: Semi-Markov process, Embedded Markov chain, Loss probability, Heterogeneous servers, Queueing systems
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Dokuz Eylül Üniversitesi Adresli: Evet
Özet
In this study, a queuing system of K-capacity with recurrent entry and three heterogeneous servers has been investigated. In the system discussed, inter-arrival times are independent of one another and have an arbitrary distribution. The service time of each server has an Exponential distribution with parameter mu(k). The customer who enters the system starts to receive service on the server with the lowest index number from the servers that are empty. If all servers are busy on arrival, the incoming customer joins the queue. When the system is at full capacity, the incoming customer leaves the system without receiving any service. The system under consideration was modeled using a semi-Markov process and the embedded Markov chain provided by the semi-Markov process was obtained. Steady-state probabilities and the probability of customer loss were calculated. Additionally, by performing optimization with respect to service discipline and arrival process, the loss probability is minimized. The obtained theoretical results are shown numerically for cases where the inter-arrival times followed Exponential, Erlang, and deterministic distributions.