Transient solution of multiple vacation queue with discouragement and feedback

Abstract

Congestion problems with processor vacations are characterized by high intricacy and explicit transient solutions to these problems are exceptionally difficult to apply. These solutions are essential to studying the dynamic behavior of computing systems over a finite period and they are predominantly utilized within a state-of-theart design architecture for a real-time I/O system. Motivated by the above finding, this study adopts mathematical concepts, namely continued fractions and generating function, to derive explicit expressions for transient-state probabilities. Transient-state probabilities of the processing delay problem with a single processor, which adopts the multiple-vacation policy to save power consumption and thermal trip error with discouragement and feedback, are obtained in terms of modified Bessel functions using the properties of the confluent hypergeometric function. Given the inaccessibility of the processor, discouraging behaviors like balking and reneging on job requests are likely to appear. Routing back for the service feedback for the processed job request is also critical to maintaining Quality of Service (QoS). Considering the performance of the I/O system, the expected value of the state of the computing system using stationary queue-size distribution is derived.