End-to-End Latency Evaluation of the Sat5G Network Based on Stochastic Network Calculus

Simultaneous use of heterogeneous radio access technologies to increase the performance of real-time,reliability and capacity is an inherent feature of satellite-5G integrated network(Sat5G).However,there is still a lack of theoretical characterization of whether the network can satisfy the end-to-end transmission performance for latency-sensitive service.To this end,we build a tandem model considering the connection relationship between the various components in Sat5G network architecture,and give an end-to-end latency calculation function based on this model.By introducing stochastic network calculus,we derive the relationship between the end-to-end latency bound and the violation probability considering the traffic characteristics of multimedia.Numerical results demonstrate the impact of different burst states and different service rates on this relationship,which means the higher the burst of arrival traffic and the higher the average rate of arrival traffic,the greater the probability of end-to-end latency violation.The results will provide valuable guidelines for the traffic control and cache management in Sat5G network.

On applying stochastic network calculus

Performance evaluation plays a crucial role in the design of network systems. Many theoretical tools, including queueing theory, effective bandwidth and network calculus, have been proposed to provide modeling mechanisms and resuits. While these theories have been widely adopted for performance evaluation, each has its own limitation. With that network systems have become more complex and harder to describe, where a lot of uncertainty and randomness exists, to make performance evaluation of such systems tractable, some compromise is often necessary and helpful. Stochas- tic network calculus （SNC） is such a theoretical tool. While SNC is a relatively new theory, it is gaining increasing interest and popularity. In the current SNC literature, much attention has been paid on the development of the theory itself. In addition, researchers have also started applying SNC to performance analysis of various types of systems in recent years. The aim of this paper is to provide a tutorial on the new theoretical tool. Specifically, various SNC traffic models and SNC server models are reviewed. The focus is on how to apply SNC, for which, four critical steps are formalized and discussed. In addition, a list of SNC application topics/areas, where there may exist huge research potential, is presented.

On the Backlog and Delay Distributions of Primary and Secondary Users in a Cognitive Radio Network

In a cognitive radio network, the secondary users can use the spectrum holes when the primary users do not utilize the spectrum, but they must vacant the spectrum when the primary users need to transmit data on the spectrum. In other words, the primary users have higher priority over the secondary users. In this paper, backlog and delay distribution bounds for both primary users and secondary users are obtained. The analysis is based on stochastic network calculus, for which, stochastic service curves are t-n-st derived for both primary users and secondary users, and the network calculus independent case analysis approach is used to find the distribution bounds. Numerical results and simulation results are also presented and discussed.

Probabilistic Delay Analysis of Internet of Things Based on LTE Network

An Long Term Evolution (LTE) network based mobile Internet of Things (IoT) is modeled and analyzed with the probabilistic delay distribution as the main interest. Stochastic network calculus is relied on to conduct the analysis. Two typical traffic models, i.e., Compound Poisson and Aggregated ON-OFF Source, are analyzed. The wireless fading channel is modeled as a Gilbert-Elliot channel. Numerical results are presented, where the probabilistic delay distribution and guaranteed capacity under certain delay constraint are shown and discussed.

Data-flow in mobile edge computing networks: end-to-end performance analysis using stochastic network calculus

Mobile edge computing(MEC) networks can provide a variety of services for different applications. End-to-end performance analysis of these services serves as a benchmark for the efficient planning of network resource allocation and routing strategies. In this paper, a performance analysis framework is proposed for the end-to-end data-flows in MEC networks based on stochastic network calculus(SNC). Due to the random nature of routing in MEC networks, probability parameters are introduced in the proposed analysis model to characterize this randomness into the derived expressions. Taking actual communication scenarios into consideration, the end-to-end performance of three network data-flows is analyzed, namely, voice over Internet protocol(VoIP), video, and file transfer protocol(FTP). These network data-flows adopt the preemptive priority scheduling scheme. Based on the arrival processes of these three data-flows, the effect of interference on their performances and the service capacity of each node in the MEC networks, closed-form expressions are derived for showing the relationship between delay, backlog upper bounds, and violation probability of the data-flows. Analytical and simulation results show that delay and backlog performances of the data-flows are influenced by the number of hops in the network and the random probability parameters of interference-flow(IF).

Conditional Stability of Stochastic Volterra Equationswith Anticipating Kernel

This paper introdnces some concepts of conditional stability of stochasticVolterra equations with anticipating kernel. Snfficient conditions of these types of sta-bility are established via Lyapunov funciton.

A Donsker Delta Functional Approach to Optimal Insider Control and Applications to Finance

We study optimal insider control problems,i.e.,optimal control problems of stochastic systemswhere the controller at any time t,in addition to knowledge about the history of the system up to this time,also has additional information related to a future value of the system.Since this puts the associated controlled systems outside the context of semimartingales,we apply anticipative white noise analysis,including forward integration and Hida-Malliavin calculus to study the problem.Combining this with Donsker delta functionals,we transform the insider control problem into a classical(but parametrised)adapted control system,albeit with a non-classical performance functional.We establish a sufficient and a necessary maximum principle for such systems.Then we apply the results to obtain explicit solutions for some optimal insider portfolio problems in financial markets described by Itô-Lévy processes.Finally,in the Appendix,we give a brief survey of the concepts and results we need from the theory of white noise,forward integrals and Hida-Malliavin calculus.

Phase noise analysis of oscillators with Sylvester representation for periodic time-varying modulus matrix by regular perturbations

Phase noise analysis of an oscillator is implemented with its periodic time-varying small signal state equations by perturbing the autonomous large signal state equations of the oscillator. In this paper, the time domain steady solutions of oscillators are perturbed with traditional regular method; the periodic time-varying Jocobian modulus matrices are decomposed with Sylvester theorem, and on the resulting space spanned by periodic vectors, the conditions under which the oscillator holds periodic steady states with any perturbations are analyzed. In this paper, stochastic calculus is applied to disclose the generation process of phase noise and calculate the phase jitter of the oscillator by injecting a pseudo sinusoidal signal in frequency domain, representing the white noise, and a δcorrelation signal in time domain into the oscillator. Applying the principle of frequency modulation, we learned how the power-law and the Lorentzian spectrums are formed. Their relations and the Lorentzian spectrums of harmonics are also worked out. Based on the periodic Jacobian modulus matrix, the simple algorithms for Floquet exponents and phase noise are constructed, as well as a simple case is demonstrated. The analysis difficulties and the future directions for the phase noise of oscillators are also pointed out at the end.

A STRASSEN LAW OF THE ITERATED LOGARITHM FOR PROCESSES WITH INDEPENDENT INCREMENT

Let X={X(t),t 0} be a process with independent increments (PII)such that E=0, D X(t)E 2<∞, lim t→∞D X(t)t=1, and there exists a majoring measure G for the jump △X of X . Under these assumptions, using rather a direct method, a Strassen's law of the iterated logarithm (Strassen LIL) is established. As some special cases,the Strassen LIL for homogeneous PII and for partial sum process of i.i.d.random variables are comprised.

Limit behaviour of the minimal solution of a BSDE with singular terminal condition in the non Markovian setting

We use the functional Ito calculus to prove that the solution of a BSDE with singular terminal condition verifies at the terminal time:lim inf_(t→T)Y(t)=ξ=Y(T).Hence,we extend known results for a non-Markovian terminal condition.