2015/11/16 by David Aldous, Aldous, David
Business, Management and Accounting · Mathematics · #60J05 #60J70 #60K25 #Advanced Queuing Theory Analysis #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1511.05140
openalex publication_date 2015/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We model a long queue of humans by a continuous-space model in which, when a customer moves forward, they stop a random distance behind the previous customer, but do not move at all if their distance behind the previous customer is below a threshold. The latter assumption leads to ``waves" of motion in which only some random number W of customers move. We prove that Pr(W > k) decreases as order k-1/2; in other words, for large k the k'th customer moves on average only once every order k1/2 service times. A more refined analysis relies on a non-obvious asymptotic relation to the coalescing Brownian motion process; we give a careful outline of such an analysis without attending to all the technical details.