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...

Corresponding Author: Adeeb Alsaaidah Faculty of Science and Technology, Universiti Sains Islam Malaysia (USIM), Nilai, Malaysia Email:[email protected] Abstract: This paper presents a performance study for Gentle BLUE (GB) under the bursty and correlated properties of aggregated network traffic. The Bernoulli Process (BP) fails to represent the properties of aggregated correlated and bursty ...

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...

In this paper, we proposed a new multistage virtual shared memory model for cluster based parallel systems. This model can be expanded in hierarchical manner and covered many of the previous clusters of parallel system designs. Queuing theory and Jackson queuing networks are applied for constructing an analytical model. This model gives a closed-form solution for the system performance metrics,...

In this paper, we use both fuzzy optimization and normal simulation methods to solve fuzzy web planning model problems, which are queuing system problems for designing web servers. We apply fuzzy probabilities to the queuing system models with customers arrival rate λ and servers’ service rate μ, and then compute fuzzy system performance variables, including Utilization, Number (of requests) in...