• Media type: E-Article
  • Title: On the waiting time of a two-stage queueing system with blocking
  • Contributor: Langaris, Christos; Conolly, Brian
  • Source: Journal of Applied Probability ; 21 ( 1984 ) S. 628-638
  • Published: Cambridge University Press (CUP), 1984
  • Language: English
  • DOI: 10.2307/3213623
  • ISSN: 0021-9002; 1475-6072
  • Keywords: Statistics, Probability and Uncertainty ; General Mathematics ; Statistics and Probability
  • Abstract: <jats:p>An analysis is given of the first-come-first-served waiting-time process in stages 1 and 2 of a two-stage service system with <jats:italic>k</jats:italic> and <jats:italic>n</jats:italic> parallel service channels in the first and second stages respectively, and <jats:italic>m</jats:italic> intermediate waiting places (<jats:italic>k, n</jats:italic> ≧ 1, <jats:italic>m</jats:italic> ≧ 0).</jats:p><jats:p>Although the method of analysis is straightforward the details are intricate and require careful study of the location of the zeros of a high-degree polynomial.</jats:p><jats:p>The analysis paves the way for an extensive study of the numerical effect on waiting time of blocking in commonly encountered systems of this nature. ‘Effective service time' in stage 1, defined so as to include blocked time, is considered separately.</jats:p>
  • Description: <jats:p>An analysis is given of the first-come-first-served waiting-time process in stages 1 and 2 of a two-stage service system with <jats:italic>k</jats:italic> and <jats:italic>n</jats:italic> parallel service channels in the first and second stages respectively, and <jats:italic>m</jats:italic> intermediate waiting places (<jats:italic>k, n</jats:italic> ≧ 1, <jats:italic>m</jats:italic> ≧ 0).</jats:p><jats:p>Although the method of analysis is straightforward the details are intricate and require careful study of the location of the zeros of a high-degree polynomial.</jats:p><jats:p>The analysis paves the way for an extensive study of the numerical effect on waiting time of blocking in commonly encountered systems of this nature. ‘Effective service time' in stage 1, defined so as to include blocked time, is considered separately.</jats:p>