MxG1 Vacation Queueing Models With Bilevel Thresholds Multifarious Services Immediate Feedbacks And Service Interruptions

Abstract

In chapter 1, definitions of various characteristics of queueing process, descriptions of the models newlineunder consideration, review of literature, methodology and some preliminary results are presented.In newlineChapter II,it is assumed thata cycle starts whenever the system empties and the server is deactivated and newlineleaves the system immediately for vacation of random length.The server operates (m, N)-policy with at most newlineJ-multiplevacations.During busy period,the server provides singleFES to allarriving customers in the first newlinephase and C-optional heterogeneous services in the second phase.As soon as the FES is completed, each newlinecustomer may either opt for a certain (ith)service in the second phase (with probability ri, 0 and#61603; riand#61603; 1) or may newlineleave the system(with probability(1 r )) newlineC newlinei 1 newlinei and#61669; newlineand#61501; newlineand#61485; .The server is subject to random breakdowns during busy newlineperiod and the server s lifetime follows the exponential distribution in the first phase with parameter a. In newlinethe second phase, the server fails at an exponentialrate ai(1 and#61603; i and#61603; C).Wheneverbreakdowns occur,it is newlineassumed that the server is sent for repair immediately. The customer,just being served just before newlinebreakdown, waits for the server to return from the repair facility to complete the remaining service. As soon newlineas the server is fixed,the service resumes for the waiting customer. The vacation period,buildup period,setup newlineperiod,dormant period,busy period and breakdown period constitute a cycle for the model.The model newlineanalyzed in chapter III differs from the model of chapter II, in service facility and the customers behaviour newlineduring breakdown period. The author scrutinizes the (m, N)-policy by considering three possible scenarios newlineto restoring an interrupted service together in a single MX/G/1 queueing system. They include, if the server newlinefails,then the customer in service mayjoin the head of the queue and opt for a new service (with probability newlineq1) or may leave the system without completing the service (with probability q2) or else stay in the service newlinefacility (with probability q3