Queueing Systems

, Volume 39, Issue 2–3, pp 213–256

Asymptotic Expansions for the Congestion Period for the M/M/∞ Queue

  • Charles Knessl
  • Yongzhi Peter Yang


We consider the M/M/∞ queue with arrival rate λ, service rate μ and traffic intensity ρ=λ/μ. We analyze the first passage distribution of the time the number of customers N(t) reaches the level c, starting from N(0)=m>c. If m=c+1 we refer to this time period as the congestion period above the level c. We give detailed asymptotic expansions for the distribution of this first passage time for ρ→∞, various ranges of m and c, and several different time scales. Numerical studies back up the asymptotic results.

M/M/∞ queue busy period asymptotics 


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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Charles Knessl
    • 1
  • Yongzhi Peter Yang
    • 2
  1. 1.Department of Mathematics, Statistics and Computer Science (M/C 249)University of Illinois at ChicagoChicagoUSA
  2. 2.Department of MathematicsUniversity of St. ThomasSt. PaulUSA

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