Numerical Study of Queuing-Inventory Systems with Catastrophes under Base Stock Policy
We consider a single-server queuing-inventory system (QIS) with catastrophes under the base stock policy. Consumer customers (c-customers) that arrived to buy inventory, can be form of queue in an infinite buffer. All items in the warehouse are destroyed if a catastrophe is occurring, but in such cases the c-customers in the system (on the server or in the buffer) are still waiting to be restocked. Upon arrival of negative customer (n-customer) one c-customer is pushed out, if any. A hybrid sale rule is used: if upon arrival of the c-customer, the inventory level is zero, then according to the Bernoulli scheme, this customer is either lost (lost sale rule) or it is joining to the queue (backorder rule). Mathematical model of the investigated QIS is constructed as two-dimensional Markov chain (2D MC). Ergodicity condition is established, and the matrix-analytic method (MAM) is used to calculate the steady-state probabilities of the constructed 2D MC. Formulas for performance measures are found and the results of numerical experiments are illustrated.