Modeling And Analyzing A Queueing System With Admission Control And Maintenance Policy

Based on the background of actual manufacturing systems,this dissertation proposes an M/G/1 queueing system model with admission control and maintenance policy,in which when the system becomes empty,the maintenance workman immediately conduct a maintenance on the system and only D(a given threshold)customers are allowed to enter the system during the maintenance time,D≥ 1.Employing the renewal process theory and total probability decomposition technique,we carry out a detailed analysis on the transient and equilibrium properties of the queue size at any time t.Some important queueing and reliability performance measures of the system are obtained.Under a given cost structure,numerical examples are provided to discuss the one-dimensional optional control strategy and the twodimensional optional control strategy for economizing the system cost.This dissertation is divided into the following two chapters:1)In the first chapter of this dissertation,based on the background of actual manufacturing systems,we propose a new queueing model—an M/G/1 queueing system model with admission control and maintenance policy by introducing admission control and maintenance policy.In this system,as soon as the system becomes empty,it is closed immediately and a routine maintenance action is carried out for a random time length Y where at most D(≥ 1)customers are allowed to enter the system during system’s maintenance period Y.First of all,under any initial state,we employ the renewal process theory,total probability decomposition technique and Laplace transform to discuss the transient queue length distribution of the system at any time t,and obtain the expressions of the Laplace transform of the transient queue length distribution with respect to time t.Then,the recursive formulas of the steadystate queue length distribution,which can be used to conveniently calculate the queue length distribution,are obtained by using L’Hospital’s rule.Moreover,some special cases such as D→∞ and P {Y=0}=1 are also discussed.At last,applying the renewal reward theory,the explicit expression of the long-run expected cost per unit time is presented,and numerical examples are provided to determine the one-dimensional optional control strategy D*for economizing the system cost as well as the one-dimensional optional control strategy T*and the two-dimensional optional control policy(T*,D*)when the maintenance time is a fixed length T.2)In the second chapter of this thesis,considering the real case that the service equipment may break down during the service period,this chapter establishes an M/G/1 repairable queueing model with admission control and maintenance policy by introducing“the service station may fail and it can be repaired”.In this repairable queueing model,when the repair is completed,the service station returns to a new state and operates immediately.Firstly,we define the customer’s generalized service time and the server’s generalized busy period to demonstrate that from the queueing view the repairable queueing model studied in the chapter 2 is equal to the queueing model discussed in the chapter 1 above.Then,some queueing performance indexes of the repairable queueing system are derived by the similar analytical method used in the chapter 1.Moreover,through numerical examples,we analyze the influences of the failure rate and repair rate of the service station on the admission control.Secondly,some reliability performance measures of the service station,such as the transient and steady-state unavailability,the expected failure number during(0,t]and steady-state failure frequency of the service station,are respectively discussed in detail.