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A PERISHABLE INVENTORY SYSTEM WITH SERVICE FACILITIES, MAP ARRIVALS AND PH- SERVICE TIMES

Journal of Systems Science and Systems Engineering 2007年第1期16卷 62-73页

作者： Paul MANUEL B. SIVAKUMAR G. ARIVARIGNAN Department of Information Science Kuwait University Kuwait. Department of Applied Mathematics and Statistics School of Mathematics Madurai Kamaraj University Madurai Tamilnadu India

We consider a continuous review perishable （s,S） inventory system with a service facility consisting of a waiting hall of finite capacity and a single server. We assume two types of customers, ordinary and negative, arrive according to a Markovian Arrival Process （MAP）. An ordinary customer joins the queue and a negative customer instead of joining the queue removes one ordinary customer from the queue. The removal rule adopted in this paper is RCE （removal of a customer from the end）. The individual customer＇s unit demand is satisfied after a random time of service which is assumed to have a phase-type distribution. The life time of each item and the lead time of the reorders have been assumed to be independent exponential distributions. The joint probability distribution of the number of customers in the system and the inventory level is obtained for the steady state case. Various stationary system performance measures are computed and the total expected cost rate is calculated. The results are illustrated numerically.

关键词： Stochastic inventory Markovian demands service facility positive lead time negative customers

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N-policy for M^(x)/G/1 Unreliable Retrial G-Queue with Preemptive Resume and Multi-services

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Journal of the Operations Research Society of China 2016年第4期4卷 437-459页

作者： Amita Bhagat Madhu Jain Department of Applied Sciences The Northcap UniversityGurgaon 122017India Department of Mathematics Indian Institute of Technology RoorkeeRoorkee 247667India

Bulk arrival retrial G-queue with impatient customers and multi-servicessubject to server breakdowns has been analyzed. The system allows the arrival oftwo types of customers: positive customers and negative customers in the *** negative customers make the server fail if they find the server in busy state,whereas positive customers are served if the server is idle otherwise they join thevirtual pool of customers called orbit. The customers from the retrial orbit try theirchance again for the service. The customers have the option of obtaining more than oneservice. Moreover, the customers are impatient and may renege from the system withprobability (1−r ). The server is sent for repair as soon as it breakdowns;after repair,the service process starts again. Also, the server has the provision to initiate the servicewhen there areN customers accumulated in the system. Using supplementary variablestechnique and generating functions, various performance measures like reliabilityindices and long run probabilities have been obtained.

关键词： Retrial queue N-policy vacation negative customers Reneging Bulk arrival Breakdowns Preemptive resume Multi-services

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