Numerical Study of Queuing-Inventory Systems with Catastrophes under Base Stock Policy

Prof. Agassi Melikov(Azerbaijan)

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.

About the speaker

Agassi Melikov avatar

Prof. Agassi Melikov

  • Institute of Control Systems, National Academy of Sciences of Azerbaijan

Agassi Melikov received his degree in Mathematics at Baku State University, Azerbaijan in 1977, PhD in Control Theory from Institute of Automatics, Kiev, in 1984, and Doctor of Sciences in Computer Science from Department of Applied Mathematics at Kiev National Technical University, Ukraine in 1992. He completed his dissertations under the guidance of academician Volodimir Korolyuk, Ukraine. His research interests are in the tele-traffic, queuing, inventory, reliability and their applications. He has published more than 120 papers in internationally refereed journals and more than 40 presentations at the international conferences. He is the author of five monographs, including two monographs published by Springer: Performance Analysis and Optimization of Multi-Traffic on Communication Networks (2010) and Multidimensional Queueing Models in Telecommunication Networks (2014). He was a Visiting Scholar in the Telecommunication Mathematics Research Centre at the Korea University, Seoul in 2006. He is currently Head of Department of Queuing and Queuing-Inventory Systems at Institute of Control Systems, National Academy of Sciences of Azerbaijan and Head of Department of Computer Systems and Programming at National Aviation Academy, Azerbaijan.