Generalization of the Takacs' Formula for GI/M/n/0 Queuing System with Heterogeneous Servers

İŞGÜDER H. O., UZUNOĞLU KOÇER U. Z., Celikoglu C. C.

World Congress on Engineering (WCE 2011), London, Kanada, 6 - 08 Temmuz 2011, ss.45-47 identifier identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası:
  • Basıldığı Şehir: London
  • Basıldığı Ülke: Kanada
  • Sayfa Sayıları: ss.45-47
  • Anahtar Kelimeler: Embedded Markov chain, heterogeneous servers, Laplace-Stieltjes transform, loss probability
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

This study is mainly concerned with the finite capacity queuing system with recurrent input, n heterogeneous servers, and no waiting line. In the system customers choose only one server from the empty servers with equal probability. When all servers are busy, customers depart from the system without taking any service. These customers are called "lost customers". In this study, the transition probabilities (p(ij)) of the embedded Markov chain are calculated using the generalization of the Takacs' formula. The steady-state probabilities can be obtained from pi(j) = Sigma(infinity)(i=o) pi(i)p(y) with Sigma(infinity)(j=0) pi(j) = 1. Since there is no waiting line, the loss probability (P-L) is equal to the probability that all servers are busy.