A.Z. Melikov, M.O. Shahmaliyev
Analysis of perishable queueing-inventory system with MMPP flow and different types of customers


Perishable queueing-inventory system with positive service time and different types of customers is considered. Customers are arriving according to the Markov-Modulated Poisson process (MMPP). The inventory size is finite, while the queue length is infinite. Customers after the service completion either purchase the inventory item or leave the system empty-handed. The inventory items perish independently after exponentially distributed random times. The customers in the queue become impatient when the inventory level drops to zero. Impatient customers according to Bernoulli trial leave the system after exponentially distributed random times. If there are no items left in the inventory at the moment of arrival, the customer either enters the queue or leaves the system according to Bernoulli scheme. The (s, S) policy is used for the inventory replenishment. Gillespie’s Direct simulation method is used to calculate the stationary distribution and performance measures of the system. The convergence speed of simulation, dependence of performance measures on reorder level and solution of optimization problem are considered and illustrated in the numerical experiment.

Keywords:
Perishable queuing-inventory system, Infinite 3D Markov Chain, Stationary distribution, Simulation algorithm, (s, S) replenishment policy, Numerical experiments, MMPP flow, Total run cost optimization
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