Tail behaviour of the area under a random process, with applications to queueing systems, insurance and percolations

2011/02/05 by Rafał Kulik, Kulik, Rafal, Zbigniew Palmowski +1
Decision Sciences · Business, Management and Accounting · Mathematics · #Probability and Risk Models #Advanced Queuing Theory Analysis #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1102.1095

Abstract

The areas under workload process and under queuing process in a single server queue over the busy period have many applications not only in queuing theory but also in risk theory or percolation theory. We focus here on the tail behaviour of distribution of these two integrals. We present various open problems and conjectures, which are supported by partial results for some special cases.

Citations

• Random difference equations and Renewal theory for products of random matrices

Related

• Tail Probabilities in Queueing Processes
• Infinite Servers with Poisson Arrivals Queue Busy Period with PME Distribution
• QUEUE, with Poisson arrivals, constant service time and infinite\n servers, BUSY PERIOD DISTRIBUTION
• Tail Behavoir of sums of random components
• Functional limit theorems for the number of busy servers in a G/G/∞ queue