Heavy outgoing call asymptotics for MMPP|M|1 retrial queue with two way communication and multiple types of outgoing calls

In this paper, we consider a single server retrial queue MMPP|M|1 with two way communication and multiple types of outgoing calls. Calls received by the system occupy the device for operating, if it is free, or are sent to orbit, where they make a random delay before the next attempt to occupy the device. The duration of the delay has an exponential distribution. The main issue of this model is an existence of various types of outgoing calls in the system. The intensity of outgoing calls is different for different types of outgoing calls. The operating time of the outgoing calls also differs depending on the type and is exponential random variable, the parameters of which in the general case do not coincide. The device generates calls from the outside only when it does not operate the calls received from the flow. We use asymptotic analysis methods under two limit conditions: high rate of outgoing calls and low rate of serving outgoing calls. The aim of the current research is to derive an asymptotic stationary probability distribution of the number of incoming calls in the system that arrived from the flow, without taking into account the outgoing call if it is operated on the device. In this paper, we obtain asymptotic characteristic function under aforementioned limit conditions. In the limiting condition of high intensity of outgoing calls, the asymptotic characteristic function of the number of incoming calls in a system with repeated calls and multiple types of outgoing calls is a characteristic function of a Gaussian random variable. The type of the asymptotic characteristic function of the number of incoming calls in the system under study in the limiting condition of long-term operation of the outgoing calls is uniquely determined.

Asymptotic Analysis of the MMРР|M|1 Retrial Queue with Negative Calls under the Heavy Load Condition

In the paper, a single-server retrial queueing system with MMPP arrivals and an exponential law of the service time is studied. Unserviced calls go to an orbit and stay there during random time distributed exponentially, they access to the server according to a random multiple access protocol. In the system, a Poisson process of negative calls arrives, which delete servicing positive calls. The method of the asymptotic analysis under the heavy load condition for the system studying is proposed. It is proved that the asymptotic characteristic function of a number of calls on the orbit has the gamma distribution with the obtained parameters. The value of the system capacity is obtained, so, the condition of the system stationary mode is found. The results of a numerical comparison of the asymptotic distribution and the distribution obtained by simulation are presented. Conclusions about the method applicability area are made.

Geomagnetic Reference Map Denoising Based on Singular Entropy

To weaken the noise disturbance of GRM and improve the matching precision and matching probability of inertial/geomagnetic system, this paper proposed a method for denoising based on SVD. Firstly, from the perspective of information entropy, the singular entropy is introduced and the inner link between singular entropy and signal-to-noise ratio (SNR) is analyzed. Secondly, the method based on the asymptotic characteristic of the probabilities associated with the different singular values order (SVO) is proposed. Lastly, by utilizing practical GRM, the denoising analysis about the proposed method is demonstrated and later simulation experiments of GMN are accomplished. Simulation results show that the method is feasible and reliable.

On the existence of analytic null asymptotically flat solutions of Einstein’s vacuum field equations

This paper proves the existence of analytic solutions of the asymptotic characteristic initial value problem for Einstein’s field equations for analytic data on past null infinity and on an incoming null hypersurface.

The asymptotic characteristic initial value problem for Einstein’s vacuum field equations as an initial value problem for a first-order quasilinear symmetric hyperbolic system

The asymptotic characteristic initial value problem for Einstein’s vacuum field equations where data are given on an incoming null hypersurface and on part of past null infinity is reduced to a characteristic initial value problem for a first-order quasilinear symmetric hyperbolic system of differential equations for which existence and uniqueness of solutions can be shown. It is delineated how the same method can be applied to the standard Cauchy problems for Einstein’s vacuum and conformal vacuum equations.

On the regular and the asymptotic characteristic initial value problem for Einstein’s vacuum field equations

The regular characteristic initial value problem for Einstein’s vacuum field equations where data are given on two intersecting null hypersurfaces is reduced to a characteristic initial value problem for a symmetric hyperbolic system of differential equations. This is achieved by making use of the spin-frame formalism instead of the harmonic gauge condition. The method is applied to the asymptotic characteristic initial value problem for Einstein’s vacuum field equations, where data are given on part of past null infinity and on an incoming null-hypersurface. A uniqueness theorem for this problem is proved by showing that a solution of the problem must satisfy a regular symmetric hyperbolic system of differential equations in a neighbourhood of past null infinity.