AN INVENTORY SYSTEM WITH A STANDBY SERVER

Abstract

In this paper, we work on (s, Q) inventory queuing system for providing two types of customers services, namely high priority customer and low priority customer, with one basic server interruption and a standby server replaces whenever the basic server gets interruption. The high priority customer demands a unit item along with some services and the low priority customer demands only the services (on the used item) but not purchasing the item at that time. The high priority customers are allowed in the queue with ï¬nite capacity waiting hall and low priority customers allowed in the ï¬nite orbit with retrial policy when the server is busy, otherwise, the customer is lost. Also, in this discussion, the server can go in orbit search of customers immediately after either the inventory is stocked out or there is no queue. The customers’ arrivals of both types follow Poisson processes and the times of both the services follow the exponential distributions while the interruption times and the stand-by service times are exponentially distributed. Finally, the system performance measures are derived in the steady states.Keywords: Continuous review, Perishable commodity, Heterogeneous servers, Standby server. 

Inthispaper,weworkon(s,Q)inventoryqueuingsystemforprovidingtwotypesofcustomersservices,namelyhighprioritycustomerandlowprioritycustomer,withonebasicserverinterruptionandastandbyserverreplaceswheneverthebasicservergetsinterruption.Thehighprioritycustomerdemandsaunititemalongwithsomeservicesandthelowprioritycustomerdemandsonlytheservices(ontheuseditem)butnotpurchasingtheitematthattime.Thehighprioritycustomersareallowedinthequeuewithï¬nitecapacitywaitinghallandlowprioritycustomersallowedintheï¬niteorbitwithretrialpolicywhentheserverisbusy,otherwise,thecustomerislost.Also,inthisdiscussion,theservercangoinorbitsearchofcustomersimmediatelyaftereithertheinventoryisstockedoutorthereisnoqueue.Thecustomers’arrivalsofbothtypesfollowPoissonprocessesandthetimesofboththeservicesfollowtheexponentialdistributionswhiletheinterruptiontimesandthestand-byservicetimesareexponentiallydistributed.Finally,thesystemperformancemeasuresarederivedinthesteadystates.

Keywords:Continuousreview,Perishablecommodity,Heterogeneousservers,Standbyserver.