Analysis of K-capacity queueing system with two-heterogeneous server

İŞGÜDER H. O., Uzunoglu Kocer U.

1st International Conference Analytical and Computational Methods in Probability Theory, ACMPT 2017, Moscow, Rusya, 23 - 27 Ekim 2017, ss.23-30 identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası:
  • Doi Numarası: 10.1007/978-3-319-71504-9_3
  • Basıldığı Şehir: Moscow
  • Basıldığı Ülke: Rusya
  • Sayfa Sayıları: ss.23-30
  • Anahtar Kelimeler: Embedded Markov chain, Finite capacity queue, Heterogeneous servers, Loss probability, Stream of overflows
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

© 2017, Springer International Publishing AG.This study mainly concerned with the K-capacity queueing system with recurrent input and two heterogeneous servers. Interarrival times are independent and have an arbitrary distribution. There are two servers and server k has an exponential distribution with parameter μk. Arriving customers choose server from the empty servers with equal probability. At an arrival time the customer joins the queue when both servers are busy. In addition an arrival leaves without having service when the system capacity is achieved. The defined system is represented by semi-Markov process and embedded Markov chain is obtained. Steady-state probabilities are found and loss probability is calculated by analyzing stream of overflows. Moreover loss probabilities are computed numerically for the queueing systems where the interarrival times are assumed as exponential, Erlang and deterministic distribution.