Effect of disaster and balking on M/M/1 driven fluid queue with working vacation. (22nd November 2022)

• Record Type: Journal Article
• Authors: Jain, Madhu; Kumar, Anshul
• Is Part Of: International journal of mathematics in operational research. Volume 23:Number 3(2022)
• Page Start: 359
• Page End: 371
• Publication Date: 2022-11-22
• Subjects: fluid queue -- working vacation -- disaster -- balking -- generating function -- continued fraction; Operations research -- Mathematical models -- Periodicals; Operations research -- Mathematics -- Periodicals; Decision making -- Mathematical models -- Periodicals; 658.4033
• Languages: English
• ISSNs: 1757-5850

Abstract

The fluid models are suitable for modelling traffic when individual arrival units have little effect on the system's performance. This paper aims to study the fluid model for the queueing scenario driven by the features of vacationing server, disaster, and balking. By introducing vacation strategy to the fluid model, we can provide greater flexibility for the design and control of input and output rates. By introducing the multiple working vacation strategy to the fluid model, we can provide greater flexibility to design and control the server's vacationing time and output. Continuing fraction and generating function methodologies are used to solve the fundamental framework of differential-difference equations that regulates the operation. The steady state probabilities for the different states of the fluid model have been found explicitly. The stationary distribution of the buffer content has also been derived in terms of the modified Bessel function of the first kind.