Retrial Queuing-Inventory Systems with Delayed Feedback and Instantaneous Damaging of Items

This paper studies a Markov model of queuing-inventory system with primary, retrial, and feedback customers. Primary customers form Poisson flow, if an inventory level is positive upon their arrival, they instantly receive the items. If equal to zero arrival primary customer, then this according Bernoulli scheme, either leaves or goes into infinite buffer repeat request in future. The rate retrial constant, orbit remains its According each served customer feedbacks request. Destructive that flow cause damage Unlike customers, destructive do not require items, since, such decreases by one. adopted one two replenishment policies: (s, Q) S). In both policies, lead time random variable has exponential distribution. It shown mathematical under study was two-dimensional chain state space. Algorithms for calculating elements generating matrices constructed chains were developed, ergodicity conditions policies found. To calculate steady-state probabilities, matrix-geometric method used. Formulas found main performance measures system. results numerical experiments, including minimization total cost, are demonstrated.