Abstract. The authors propose a model of queueing-inventory system with perishable inventory and server vacations in which service times are positive random quantities. Server takes vacations if either inventory level is zero or queue is empty or both cases happen. At the end of vacation, server immediately starts serving the calls if inventory level is not zero; otherwise it takes new vacation. Calls in the queue are impatient and restocking follows the two-level policy. The method of asymptotic system analysis is developed and results of numerical experiments are presented.
Keywords: queueing-inventory system, server vacations, two-level policy, perishable inventory.
1 Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine,
e-mail: vskorol@yahoo.com.
2 Institute of Control Systems, National Academy of Sciences of Azerbaijan, Baku, Azerbaijan,
e-mail: agassi.melikov@rambler.ru.
3 International Scientific and Training Center of Information Technologies and Systems, National Academy of Sciences
of Ukraine and Ministry of Education and Sciences of Ukraine, Kyiv, Ukraine,
e-mail: laponomarenko@ukr.net.
4 Quafqaz
University, Baku, Azerbaijan,
e-mail: anar.rustamov@gmail.com.