Single-Server Queuing-Inventory Systems with Negative Customers and Catastrophes in the Warehouse

In this paper, we studied single-server models of queuing-inventory systems (QIS) with catastrophes in the warehouse part and negative customers (n-customers) service facility. Consumer (c-customers) that arrived to buy inventory can be queued an infinite buffer. Under catastrophes, all system is destroyed but (on server or buffer) are still waiting for replenishment stocks. Upon arrival n-customer one c-customer pushed out, if any. One two policies (RP) used system: either (s,S) randomized. investigated QISs, a hybrid scheme was used: upon c-customer, level zero, then according Bernoulli scheme, customer lost (lost sale scheme) joining queue (backorder scheme). Mathematical QISs were constructed as two-dimensional Markov chains (2D MC). Ergodicity conditions obtained, matrix-analytic method (MAM) calculate steady-state probabilities 2D MCs. Formulas performance measures found results numerical experiments presented.