Analysis of Finite Buffer Markovian Queue with Balking, Reneging and Working Vacations

This article presents the analysis of a finite buffer M/M/1 queue with multiple and single working vacations. The arriving customers balk (that is do not join the queue) with a probability and renege (that is leave the queue after joining) according to exponential distribution. The inter-arrival times, service times during a regular service period, service times during a vacation period and vacation times are independent and exponentially distributed random variables. Steady-state behavior of the model is considered and various performance measures, some special cases of the model and cost analysis are discussed. DOI: 10.4018/jsds.2013010101 2 International Journal of Strategic Decision Sciences, 4(1), 1-24, January-March 2013 Copyright © 2013, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. of customer satisfaction. It is more important to reduce reneging as renegers make the line seem longer for those contemplating joining and may prompt some to balk. At the same time customers become dissatisfied because of the total length of time they have to spend before being served. If customer’s decision making can be predicted, a powerful set of tools will be available to customer service managers. Models with customers’ impatience in queues have been studied extensively due to their versatility and applicability. An M/M/1 queue with customers balking and reneging has been discussed in Haight (1957) and (1959), respectively. The combined effects of balking and reneging in an M/M/1/N queue has been reported in Ancker and Gafarian (1963a, 1963b). Analytical solutions of the single-server Markovian overflow queue with balking, reneging and an additional server for longer queue have been discussed in Abou-El-Ata and Shawky (1992). Al-Seedy and Kotb (1991) studied the transient solution of the state-dependent M/M/1 queue with balking. Drekic and Woolford (2005) discussed a preemptive priority Markovian queue with state-dependent service and lower priority balking customers. Abou-EI-Ata and Hariri (1992) discussed the finite buffer multiple server queueing system with balking and reneging. Choudhury (2004) considered a single server finite buffer queueing system assuming reneging customers. Some of its variations have been studied by several authors including Abou-EI-Ata (1991), Altman and Yechiali (2008), Baccelli et al. (1984), Kok and Tijms (1985) and Shawky (1997). Queueing systems with server vacations have been studied extensively due to their wide applications in several areas including computer and communication systems, manufacturing and production systems. More details have been reported in Doshi (1986), Takagi (1991) and Tian and Zhang (2006) and Tadj and Abid (2009). In the study of vacation models, the server is generally assumed to stop service completely during vacation period. However, there are numerous situations where the server remains active during the vacation period and serves the customers generally at a slower rate. At the end of a vacation if the queue is nonempty a service period begins with normal service rate; otherwise the server takes another vacation. This policy is called multiple working vacations (MWV). Under the single working vacation (SWV) policy, the server takes only one working vacation when the system becomes empty. When the server returns from a SWV, it stays in the system waiting for customers to arrive instead of taking another working vacation. Otherwise, it changes the service rate back to the normal service rate as under the MWV policy. Servi and Finn (2002) introduced the concept of multiple working vacations with the study of M/M/1/WV queue. Wu and Takagi (2006) generalized the M/M/1/WV queue to an M/G/1/WV queue. SWV queues have been studied by Tian et al. (2008, 2010). The study of the queueing systems with balking, reneging and vacations seems to be a recent endeavor. Zhang et.al (2005) considered an M/M/1/N queue with balking, reneging and multiple server vacations. However, queueing models with server working vacations accommodate the real world situations more closely. This motivated us to study an M/M/1/N queueing system with balking, reneging and multiple and single working vacations. Performance modeling of Markovian queue with balking has attracted many researchers due to its applications in real life congestion problems. Even if a customer does not balk and joins a queueing system, customers may become impatient in the queue while waiting for service, and depart from the system after some time. Such impatient behavior is known as reneging. Many practical queueing systems with balking and reneging have been widely applied to many real-life problems such as impatient telephone switchboard customers, the hospital emergency rooms handling critical patients, and perishable goods storage in inventory systems. Balking and reneging are not only common phenomena in queues arising in routine activities, but also in telecommunication networks and in several machine repair models. This paper deals with a Markovian multiple and single working vaca22 more pages are available in the full version of this document, which may be purchased using the "Add to Cart" button on the product's webpage: www.igi-global.com/article/analysis-finite-buffer-markovianqueue/77333?camid=4v1 This title is available in InfoSci-Journals, InfoSci-Journal Disciplines Business, Administration, and Management. Recommend this product to your librarian: www.igi-global.com/e-resources/libraryrecommendation/?id=2