Cost Of Reaching With Prohibition For An Exponential Time-Sharing Queueing Process

Abstract

A process of servicing of conflict flows with a time-sharing algorithm with readjustments is considered. Input flows are formed in a random environment synchronized with the servicing device. Service and readjustment durations are exponentially distributed. A mathematical model for the servicing process is constructed in form of a denumerable continuous-time Markov chain. To estimate the loading degree of the timesharing queueing system with readjustments an expected cost of reaching with prohibition is proposed. It generalizes Chung functional for homogeneous denumerable discrete-time Markov chains. A control is searched for which minimizes the functional in a class of simple priority controls with threshold.