Single server multiple vacation queue with discouragement solve by confluent hypergeometric function
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ORIGINAL RESEARCH
Single server multiple vacation queue with discouragement solve by confluent hypergeometric function Amit Kumar1 Received: 1 April 2020 / Accepted: 8 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Waiting line problems with server vacation have envisaged with increasing complexities and their explicit transient solutions are rigorous in computations, at the same time such solutions are valued for studying the dynamical behaviour of queuing systems over a finite period predominantly utilizes within the state-of-art design process for a real time system. Keeping this fact in mind we adopt continued fractions and generating function to derive explicit expressions for transient state probabilities. In this paper, we consider the waiting line problem with a single server which adopts the multi vacations policy. We analyzed the transient part for a single server multi vacations queue with discouragement . It is also obtained the expected value of the state of the system using stationary queue size distribution, which gives a quick glance of a system performance. Keywords Multiple vacations · Balking · Reneging · Confluent hypergeometric function · Generating function · Modified Bessel function
1 Introduction Queues or waiting lines tend to exist at critical points in the customer journey in daily life and business processes. It can be experienced at service systems, computer and communication systems, manufacturing and production systems, check-in and check-out systems etc. Despite where the queue is or its perseverance, it perpetually gets the opportunity to emphatically or adversely impact the experience of customers and the proficiency of businesses or organization. Despite many benefits of well-managed queue, there are some negative effects of poorly managed queue which significantly needs improvement. A well-managed queue can cut down customer’s impatient behavior, improve the overall perception of the system, increase the conversation between client and organization, optimal service allocation, and encourage the positive word of mouth. In contrast, the poorly-managed queue can turn off the satisfactory level of the happy customer, diminish customer loyalty, decrease repeat business, decrease efficiency, and productivity.
* Amit Kumar [email protected] 1
Department of Mathematics, Birla Institute of Technology and Science Pilani, Pilani Campus, Rajasthan 333031, India
The availability of the service facility is one of the critical issue of the queue management. The scheduling of vacation of service facility is an important feature of interest in the well-managed queueing system to balance between idle time, extra cost, unavailability, etc. In vacation of service facility, the server is not serving the customers and busy in performing some secondary jobs. In general, the schedule of vacation commences whenever there is no customer in the system for service and it takes repeated vacations until, at the end of the random duration of the vacation, there is
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