M/G/1 Queueing System With Setup Time And Multiple Adaptive Vacations Under Min(N,V)-Policy Control

In this thesis,we consider the M/G/1 queueing system with setup time and multiple adaptive vacations under Min(N,V)-policy control.The content is divided into two parts as follows:(1)In the first part,the "set-up time" is introduced in the M/G/1 queueing system with multiple adaptive vacations under Min(N,V)-policy control,and then the M/G/1 queue-ing system model with setup time and multiple adaptive vacations under Min(N,V)-policy control model is established.By using the total probability decomposition technique and the Laplace transformation tool,the transient queue-length distribution and the steady queue-length distribution are discussed.Both the expressions of the Laplace transformation of the transient queue-length distribution and the recursive expressions of the steady queue-length distribu-tion are obtained.Furthermore,we present the stochastic decomposition result of the steady queue length.Moreover,some special cases,such as P {U=0}=1;P {U=0}=1 and P {H=1}=1;P {U=0}=1 and P {H=?)}=1 are discussed.(2)In the second part,on the basis of the first part,we consider the service station may be subject to failures randomly during serving customers and then is sent for repair immedi-ately.So that,the M/G/1 repairable queueing system model with setup time and multiple adaptive vacations under Min(N,V)-policy control model is also established.By defining the "generalized service time" of the customer and the "generalized busy period" of the server,we discuss some the queuing indices of the system.Meanwhile,some reliability in-dices,including the distribution of the first failure time of the service station,the transient and the steady-state unavailability of the service station,and the expected failure number of the ser-vice station breakdowns during the time interval(0,t]are emphatically discussed by using the total probability decomposition law and the Laplace transformation tool.We obtain not only the expression of the Laplace-Stieltjes(LS)transform of the first failure time distribution and the expression of the mean first failure time of the service station,but also the expression of the Laplace(L)transform of the transient unavailability at time t and the steady-state unavailability of the service station.Moreover,the expression of the Laplace-Stieltjes(LS)transform of the expected failure number during the time interval(0,t]and the expression of the steady-state failure frequency of the service station are also given.