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Effects of Reneging, Server Breakdowns and Vacation on a Batch.Arrival Single Server Queueing System with.Th.ee Fluctuating Modes of Service

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Open Journal of Optimization 2020年第4期9卷 105-128页

作者： Samuel Ugoch.kwu Enogwe h. onyebuchi obiora-ilouno Department of Statistics Michael Okpara University of Agriculture Umudike Nigeria Department of Statistics Nnamdi Azikiwe University Awka Nigeria

Th.s article examines th. effects of reneging, server breakdown and server vacation on th. various states of th. batch.arrivals queueing system with.single server providing service to customers in th.ee fluctuating modes. In th.s queueing system, any batch.arrival joins th. queue if th. server is busy or on vacation or under repair. h.wever, if th. server is free, one customer from th. arriving batch.joins th. service immediately wh.le oth.rs join th. queue. In case of server breakdown, th. customer wh.se service is interrupted returns back to th. h.ad of th. queue. As soon as th. server h.s is repaired, th. server attends to th. customer in mode 1. For th.s queueing system, customers th.t are impatient due to breakdown and server vacation may renege (leave th. queue with.ut getting service). Due to fluctuating modes of service delivery, th. system may provide service with.complete or reduced efficiency. Consequently, we construct th. math.matical model and derive th. probability generating functions of th. steady state probabilities of several states of th. system including th. steady state queue size distribution. Furth.r, we discuss some particular cases of th. proposed queueing model. We present numerical examples in order to demonstrate th. effects of server vacation and reneging on th. various states of th. system. Th. study revealed th.t an increase in reneging and a decrease in server vacation results in a decrease in server utilization and an increase in server’s idle time provided rates of server breakdown and repair completion are constant. In addition, th. probability of server vacation, th. probability of system is under repair and th. probabilities th.t th. server provides service in th.ee fluctuating modes decreases due to an increase in reneging and a decrease in vacation completion rates.

关键词： Queueing Reneging Server Vacation Server Breakdowns Fluctuating Modes of Service

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