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.

Abstract Under many scenarios where resources may be scarce or a good Quality of Service is requirement, appropriately sizing components and devices one the main challenges. New scenarios, such as IoT, mobile cloud computing, edge computing fog have emerged recently. The ability to design, model simulate those infrastructures critical dimension them correctly. Queuing theory models provide appr...

It is practically significant to research the traffic flow of intersection because the capacity of intersection affects the efficiency of highway network directly. This paper analyzes the traffic conditions of an intersection in certain urban by the methods of queuing theory and statistical experiment, sets up a corresponding mathematical model and compares it with the actual values. The result...

Process-driven spreadsheet queuing simulation is a better vehicle for understanding queue behavior than queuing theory or dedicated simulation software. Spreadsheet queuing simulation has many pedagogical benefits in a business school end-user modeling course, including developing students' intuition , giving them experience with active modeling skills, and providing access to tools. Spreadshee...