This research analyses the performance of a perishable queueing-inventory system for two commodities with optional customers demands. We assume in the article that all customers who come to the system can only purchase the first item or the second item or service (they do not purchase both items). This is the original aspect of the paper. We show the significance of the impact of optional demands on the system’s performance, which is the purpose of the paper. In this system, customers arrive, using the Markovian arrival process (MAP), to a demand for a single unit. The system is composed of a waiting hall with a limited capacity of F. The arriving customer observes the waiting hall is filled to capacity or the stock stage is zero, and they decide to leave the system. In the steady-state case, the joint probability distribution for the first commodity, the second commodity, and the number of customers in the system are computed using matrix geometric methods. We evaluate diverse system performance measures. Finally, we provide a numerical illustration of the optimal value for diverse parameters of the system, which highlights the results and implications of the article.

This paper explores the random environment with two classes of suppliers and impulse customers. The system’s greatest inventory size is S, and it has an infinitely large orbit. In this case, there are two categories of suppliers: temporary suppliers and regular suppliers. Whenever the inventory approaches r, we place on order $Q_1$ (=$S-r$) unit items to a temporary supplier. Similarly, when the inventory level drops to s (<$Q_1<r$), we place an order for $Q_2$ (=$S-s>s+1$) units of items to our regular supplier. Two types of suppliers’ lead times are considered to be exponentially distributed. Here, the customers who arrive from different states of the random environment (RE) are followed by the Markovian arrival process. If there is no inventory in the system when the customer arrives, they are automatically assigned to an orbit. The model was examined in steady state by using the matrix-analytic approach. Finally, the numerical examples for our structural model are discussed.

This article discusses the queueing-inventory model with a cancellation policy and two classes of customers. The two classes of customers are named ordinary and impulse customers. A customer who does not plan to buy the product when entering the system is called an impulse customer. Suppose the customer enters into the system to buy the product with a plan is called ordinary customer. The system consists of a pool of finite waiting areas of size N and maximum S items in the inventory. The ordinary customer can move to the pooled place if they find that the inventory is empty under the Bernoulli schedule. In such a situation, impulse customers are not allowed to enter into the pooled place. Additionally, the pooled customers buy the product whenever they find positive inventory. If the inventory level falls to s, the replenishment of Q items is to be replaced immediately under the (s, Q) ordering principle. Both arrival streams occur according to the independent Markovian arrival process (MAP), and lead time follows an exponential distribution. In addition, the system allows the cancellation of the purchased item only when there exist fewer than S items in the inventory. Here, the time between two successive cancellations of the purchased item is assumed to be exponentially distributed. The Gaver algorithm is used to obtain the stationary probability vector of the system in the steady-state. Further, the necessary numerical interpretations are investigated to enhance the proposed model.

This study investigates a multi-server queueing-inventory system in a random environment. The system has an unlimited waiting space and a maximum inventory capacity of S units. The customer arrives to the system according to the Markovian arrival process. Whenever all the servers are busy, an arriving customer either goes to an unlimited waiting space or leave the system. And if there is a free server with positive inventory, the arriving customer gets service immediately. Inventories are filled in accordance with the instantaneous replenishment policy. We consider that service time follows a phase-type distribution, and we assess the joint probability distribution of the inventory level and the number of customers in the steady state case. On top of that, we extract the sojourn and waiting time distributions of arbitrary customers using the Laplace-Stieltjes transform. Finally, a few numerical examples are provided to illustrate our mathematical model.

In this paper, we analyze two-server queueing - inventory system which consists of two-parallel queues and two category of customers i.e., high and low priority customers. The high priority customer generates demand for an item whereas the low priority customers arrive only for repair (not demanding items). Server 1 offers his service to first queue which involves only high priority customers and server 2 is a flexible server who offers his service to both the queues. When there is no availability of service in both the queues, server 1 will be at idle state whereas server 2 goes on vacation. We find a priority service rule to minimize the loss probability of low priority customers. The low priority customers will be served on threshold-based service such that a thresholdLwhich is placed in the second queue and the service starts only if the number customers in the second queue exceeds the threshold level. The limiting probability distribution of the four random variables is computed in steady state. Also, some significant change in measures of the system are derived. Finally, the suitable cost function is defined and significant numerical examples are projected.

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