Estimation of the dead time period and parameters of an asynchronous alternative flow of events with unextendable dead time period

Abstract

A problem of estimating the parameters of an asynchronous alternative flow of events with initiation of a superfluous event being a mathematical model of information flows of queries circulating in integrated service digital networks as well as a mathematical model of fluxes of elementary particles (photons, electrons, etc.) arriving at the recording equipment is considered. The conditions of flow observation are such that each registered event generates a dead time period during which other flow events are unobservable. The case of unextendable dead time period is investigated. The probability density of interarrival time in the flow under observation is found. The parameters of the initial asynchronous alternative flow with initiation of a superfluous event and a dead time period are estimated by the method of moments. Results of a statistical experiment realized for an imitational model are presented. They demonstrate fairly good properties of the estimates obtained. INTRODUCTIONIn the last two decades, an important field of application of queuing theory -design and development of information computer networks, computer communication networks, satellite communication networks, telecommunication networks, etc. lumped together as integrated service digital networks (ISDN) -has appeared in connection with the rapid development of computer and information technologies. It is quite natural that it gave impetus to the construction of new mathematical models of input flows of events describing adequately actual information flows circulating in the ISDN. We note that works [1-3] were among the first works in this direction. We emphasize, however, that in the literature devoted to queuing theory and its applications as a whole and to the ISDN in particular, only few works were devoted to adaptive service systems functioning under conditions of complete or partial uncertainty. Moreover, most authors consider situations in which all the parameters describing the input flow of events are a priori known, though this is not the case in actual situation. In practice the parameters determining the input flow of events are either known partly or unknown at all (which worsens the situation even more); they also can vary with time; moreover, the time variations are frequently random, which leads to a consideration of doubly stochastic flows of events. On the other hand, it is obvious that functioning of a service system depends directly on the parameters of the input flow of events.The random flows of events with time-dependent intensity (the doubly stochastic flows of events) can be subdivided into two classes. The flows whose intensity is a continuous random process belong to the first class. The flows whose intensity is a piecewise-constant random process with a finite number of states belong to the second class. The latter (the flows with switching or the MS flows of events [1,2]) are most typical of actual telecommunication networks. In turn, depending on the type of the state-to-state transition, the MS flows can be subd...

Optimal estimation of the states of modulated semi-synchronous integrated flow of events in condition of its incomplete observability

“…In such situations, the use of adaptive queueing systems, when the unknown stream parameters or states are estimated during the system operation and the service procedure is changed correspondingly, seems to be more rational. That is why, the central problems faced when modeling these processes are: 1) flow states estimation on monitoring the time moments of the events occurrence (filtering of underlying and unobservable intensity process) [14]; 2) flow parameters estimation on monitoring the time moments of the events occurrence [15].…”