M/M/$c$ Queues and the Poisson Clumping Heuristic

Abstract

In continuous time, customers arrive at random. Each waits until one of $c$ servers is available; each thereafter departs at random. The distribution of maximum line length of idle customers was studied over 25 years ago. We revisit two good approximations of this, employing a discrete Gumbel formulation and detailed graphics to describe simulation outcomes.

12 pages, 10 figures

References in corpus (3)

• The Maximum of an Asymmetric Simple Random Walk with Reflection
• Traffic Light Queues and the Poisson Clumping Heuristic
• Geo/Geo/2 Queues and the Poisson Clumping Heuristic

Cited by in corpus (1)

• How Long Might We Wait at Random?