On Equilibrium in a Constant Retrial Queuing System with Reserved Time and Vacations

This paper investigates an M/M/1 constant retrial queue with reserved time and vacations.A new arriving customer will take up the server and accept service immediately if the server is idle.Otherwise,if the server is busy or on vacation,customers have to join a retrial orbit and wait for retry.Once a service is completed,the server will reserve a random time to seek a customer from the orbit at a constant retrial rate.If there is no arrivals(from the orbit or outside)during the idle period,to save energy,the server will take a vacation.This paper studies the fully unobservable case.First,the steady-state condition of the system is analyzed by using the Foster’s criterion,and the customers’expected waiting time is obtained based on the generating function technique.And then,by introducing an appropriate revenue structure,the equilibrium strategies of customers and the socially optimal strategy are all derived.Furthermore,a comparison between them is made and the effect of some main system parameters is studied.

Probabilistic Model of Technical Queuing Systems with Subsystems for Detection and Recovery of Failures

The given article presents an analytical model developed for a multichannel technical queuing system with time redundancy for operability management, subsystems of reliable periodical control of sudden and gradual failure detection and a subsystem for system recovery after failure. It is assumed in the model that the failures are governed by the Poisson probability distribution law and the times of reliable control and system recovery after failures are governed by an arbitrary law of probability distribution, in the general case depending on the number of servicers. The paper defines probabilities of accomplishment of certain task volumes by the system within a priori defined time intervals, taking into consideration its reliability characteristics.