Параметры публикации

Тип публикации: 

Статья в журнале/сборнике


Analysis of a Batch Arrival, Batch Service Queuing-Inventory System with Processing of Inventory While on Vacation

Электронная публикация: 






Наименование источника: 

  • Mathematics

Обозначение и номер тома: 

9(4), 419


  • Basel


  • MDPI

Год издания: 



1-29 https://www.mdpi.com/2227-7390/9/4/419
A single-server queuing-inventory system in which arrivals are governed by a batch Markovian arrival process and successive arrival batch sizes form a finite first-order Markov chain is considered in this paper. Service is provided in batches according to a batch Markovian service process, with consecutive service batch sizes forming a finite first-order Markov chain. A service starts for the next batch on completion of the current service, provided that inventory is available at that epoch; otherwise, there will be a delay in starting the next service. When the service of a batch is completed, the inventory decreases by 1 unit, irrespective of batch size. A control policy in which the server goes on vacation when a service process is frozen until a quorum can initiate the next batch service is proposed to ensure idle-time utilization. During the vacation, the server produces inventory (items) for future services until it hits a specified level L or until the number of customers in the system reaches a maximum service batch size N, with whichever occurring first. In the former case, a server stays idle once the processed inventory level reaches L until the number of customers reaches (or even exceeds because of batch arrival) a maximum service batch size N. The time required for processing one unit of inventory follows a phase-type distribution. In this paper, the steady-state probability vector of this infinite system is computed. The distributions of inventory processing time in a vacation cycle, idle time in a vacation cycle, and vacation cycle length are found. The effect of correlation in successive inter-arrival times and service times on performance measures for such a queuing system is illustrated with a numerical example. An optimization problem is considered. The proposed system is then compared with a queuing-inventory system without the Markov-dependent assumption on successive arrivals as well as service batch sizes using numerical examples.

Библиографическая ссылка: 

Кришнамурти А.., Joshua A.N., Козырев Д.В. Analysis of a Batch Arrival, Batch Service Queuing-Inventory System with Processing of Inventory While on Vacation // Mathematics. 2021. 9(4), 419. С. 1-29 https://www.mdpi.com/2227-7390/9/4/419.