Asymptotic Expansions for the Congestion Period for the M/M/∞ Queue
- Cite this article as:
- Knessl, C. & Yang, Y.P. Queueing Systems (2001) 39: 213. doi:10.1023/A:1012752719211
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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.