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On(s,S)inventory system with random lead time and repeateddemands

机译：具有随机提前期和重复需求的库存系统

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We consider an(s,S)inventory system with random lead time and repeated demands of unsatisfied demands from the orbit. Whenever the inventory level falls to the levels, an order is placed to bring the level toS. The quantity ordered isM=S−s. Demands to the system are served immediately if there is a positive inventory. Otherwise it will go to a pool of unsatisfied customers called orbit. After a random amount of time, that demand is retried for service. We assume a Markovian setup for the time between consecutive arrivals, replenishments, and retrials. We obtained the condition for ergodicity of the system, steady state system size probabilities, expected length of the busy period of the system, expected inventory level, expected number of customers waiting in the orbit, expected waiting times, and so forth. A control problem is studied and some numerical illusrtations are provided.
机译：我们考虑一个具有随机提前期和重复满足轨道需求的需求的库存系统。每当库存水平下降到该水平时，都会下订单以将该水平提高到S。订购数量为M = SS。如果存在正库存，则将立即满足对系统的需求。否则，它将进入不满意的客户群，称为“轨道”。经过一段随机的时间后，将重试该需求以进行服务。我们假设在连续到达，补货和重试之间的时间采用马尔可夫模型。我们获得了系统遍历性，稳态系统大小概率，系统繁忙时段的预期长度，预期库存水平，预期在轨客户数量，预期等待时间等条件。研究了控制问题，并提供了一些数值说明。

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