THE CRITICAL GREEDY SERVER ON THE INTEGERS IS RECURRENT
成果类型：
Article
署名作者：
Cruise, James R.; Wade, Andrew R.
署名单位：
Heriot Watt University; Durham University
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/18-AAP1434
发表日期：
2019
页码：
1233-1261
关键词：
摘要：
Each site of Z hosts a queue with arrival rate lambda. A single server, starting at the origin, serves its current queue at rate mu until that queue is empty, and then moves to the longest neighbouring queue. In the critical case lambda = mu, we show that the server returns to every site infinitely often. We also give a sharp iterated logarithm result for the server's position. Important ingredients in the proofs are that the times between successive queues being emptied exhibit doubly exponential growth, and that the probability that the server changes its direction is asymptotically equal to 1/4.