Analysis of stationary fluid queue driven by state-dependent birth-death process subject to catastrophes

• Published in: Scientia Iranica Vol. 31; no. 14; pp. 1149 - 1158
• Main Authors: Ammar, S I, Samanta, S K, Kilany, N M, Jiang, T
• Format: Journal Article
• Language: English
• Published: Tehran Sharif University of Technology 01.07.2024
• Subjects: Behavior; Birth; Catastrophes; Communication; Communications systems; Customer services; Death; Disasters; Markov processes; Mortality; Packet transmission; Probability distribution; Queuing theory; Service facilities
• ISSN: 1026-3098; 2345-3605
• DOI: 10.24200/sci.2022.57036.5030

This paper investigates an infinite buffer fluid queueing model driven by a state-dependent birth-death process prone to catastrophes. We use the Laplace-Stieltjes transform and continued fraction approaches to establish precise expression for the joint probability of the content of the bu er and the number of customers in an M/M/1 queueing model. The importance of the proposed system is that, in numerous practical situation, the service facility has defence mechanisms in place to deal with long waits. Under the strain of a significant backlog of work, the servers may improve their service rate. Therefore, considering the state-dependent character of queueing systems is of relevance. For example, congestion control technologies prevent long queues forming in computer and communication systems by adjusting packet transmission speeds based on the length of the queue (of packets) at the source or destination. Theoretical results are supported by numerical illustrations. KEYWORDS Birth-death process; Catastrophes; Continued fraction; Fluid queue; Laplace-Stieltjes transform.