Queueing-inventory models have many practical applications and have been studied extensively in the literature. Most of the studies focus on models in which the demands occur singly. Only a very few papers analyze models wherein the demands occur in batches. In this paper we consider batch demands in the context of two models, both of which assume that the demands occur according to a versatile Markovian point process. The demands need to be serviced with items from the inventory, and the service times are assumed to be of phase type. The replenishment of the inventory is based on the (s, S)-type policy and the lead times are assumed to be random. These two models are such that in the first model an arriving customer finding the inventory level to be zero will be lost; and in the second model a customer can be lost either at the time of an arrival (wherein the server is idle due to zero inventory) or at the time of a service completion (at which time the inventory level becomes zero). In the second model, all waiting customers are removed from the system due to zero inventory. These two models are studied in steady-state using the classical matrix-analytic methods in single server case, and in the case of multi-server systems we resort to simulation using ARENA. Illustrative examples, including an optimization problem, comparing the two models are presented.

排队库存模型有许多实际应用，并且已经在文献中进行了广泛的研究。大多数研究关注的是单独出现需求的模型。只有极少数的论文分析了其中需求成批出现的模型。在本文中，我们在两个模型的背景下考虑批次需求，这两个模型均假设需求是根据通用的马尔可夫点过程发生的。需要使用库存中的物料来满足需求，并且假定维修时间属于阶段类型。库存的补货基于（s，S）类型的政策和提前期被假定为随机的。这两个模型使得在第一个模型中，到达库存水平为零的到达客户将丢失；在第二种模型中，客户可能会在到达时（其中服务器由于零库存而处于闲置状态）或在服务完成时（库存水平变为零）丢失客户。在第二种模型中，由于库存为零，因此将所有等待中的客户从系统中删除。在单服务器情况下，使用经典矩阵分析方法在稳态下研究了这两个模型，在多服务器系统的情况下，我们求助于使用ARENA进行仿真。给出了包括优化问题在内的说明性示例，将两个模型进行了比较。