Analysis Of M/M/1 Repairable Queuing System With Variable System Parameters

Repairable queuing model is a kind of queuing model which considers the performance of service desk,and it is an important research direction of queuing theory in the near future.In practical production,the system parameters of stochastic service system are often variable or adjustable,such as the failure rate can change with the state of the machine,and the repair rate can be adjusted according to the service demand.In this thesis,a single service desk repairable queuing system with variable service rate,failure rate and repair rate is studied.Various steady-state performance indexes of the system are obtained,and numerical experiments are carried out.It provides theoretical basis and numerical reference for service system optimization,and has certain practical significance.The thesis includes the following:Firstly,the M/M/1 repairable queuing system with variable service rate and failure rate is studied.According to the theory of quasi birth and death process,the state transition ma-trix of the system is obtained.The matrix equation is solved by using the method of matrix geometric solution,and the steady-state boundary probability of the system is obtained,and the reliability indexes such as the steady-state availability of the help desk are further ob-tained.Through numerical experiments,the influence of service rate and failure rate on the steady-state average queue length of the system is analyzed.Secondly,the M/M/1 repairable queuing system with variable failure rate and repair rate is studied.The system state transition matrix is obtained by the theory of quasi birth and death process.With the change of repair rate,the steady-state boundary probability of segmented system is obtained,and then the steady-state failure rate of service desk is obtained.Furthermore,the steady-state average queue length of the given repair rate change threshold is obtained.Through numerical experiments,the influence of failure rate and repair rate on the steady-state average queue length of the system is analyzed.Finally,the M/M/1 repairable queuing system with variable service rate,failure rate and repair rate is studied.The steady-state boundary probability of the system is obtained by the method of matrix geometric solution,and then the steady-state average queue length of the system is obtained.The change rule of service rate is generalized,and the steady-state average queue length of the system with two different service rate threshold is obtained.The effects of service rate,failure rate and repair rate on the steady-state average queue length of the system are analyzed by numerical experiments.