Queues, stores, and tableaux
Queues, stores, and tableaux
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队列、商店和场景
DOI：
10.1239/jap/1134587823
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
N. O’Connell
中科院分区：
文献类型：
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作者：
M. Draief;J. Mairesse;N. O’Connell
考虑具有无限缓冲区和先进先出规则的单服务台排队，M/M/1或Geom/Geom/1类型。用A表示到达过程，用S表示服务。假定满足稳定性条件。用D表示均衡的离开过程，用r表示顾客在排队最后面所花费的时间。我们证明了(D，r)与(A，S)具有相同的定律，它是经典伯克定理的推广。事实上，r可以被视为与双存储模型的背离。在利用RSK算法研究串联的瞬时行为时，这两个模型之间的这种对偶性也出现了：得到的半标准Young Tableau的第一行和最后一行分别是队列中的最后一个离开时刻和商店中的离开总数。
Consider the single server queue with an infinite buffer and a FIFO discipline, either of type M/M/1 or Geom/Geom/1. Denote by A the arrival process and by s the services. Assume the stability condition to be satisfied. Denote by D the departure process in equilibrium and by r the time spent by the customers at the very back of the queue. We prove that (D,r) has the same law as (A,s) which is an extension of the classical Burke Theorem. In fact, r can be viewed as the departures from a dual storage model. This duality between the two models also appears when studying the transient behavior of a tandem by means of the RSK algorithm: the first and last row of the resulting semi-standard Young tableau are respectively the last instant of departure in the queue and the total number of departures in the store.