The M/M/1Queuing Model And Research In Three Variable Environment

Lu Chuanlai in [1] on a single service window waiting M\/M\/1queueing modeland changeable service rate M\/M\/1queueing model, and obtains the K ’s algebraicequations using the system state, the stationary distribution and index system; WangHaitao in the literature of the [2] Service Queueing System in two mutually change theenvironment of M\/M\/1, and use the QBD process and the probability generatingfunction and its Laplasse transform tool, the system is in a steady-state probability,different initial conditions the transient probability, correlation index probabilitygenerating function and system.desk work environment is divided into A, B and C, as in A and B environments foreach parameter α （>0）and β （>0）the negative exponential distribution, while in theA and C environment of each parameter isγ （>0）andσ （>0）the negative exponentialdistribution, while in the B and C environment respectively to parameters ε （>0） andη （>0）the negative exponential distribution,The customer accepts the service time ofeach parameter forμ₁（>0）、μ₂（>0），μ₃（>0）the negative exponential distribution.According to the quasi birth and death process and probability generating function andits Laplasse transform tool, a detailed study of the following questions:1system at different initial conditions, t moment all environmental conditionsprobability.2system the probability generating function of the expression and the system on thelength distribution.3the system in different environment indicators, including the system has an averagelength, average system waiting for long time, customers in the system, system ofcustomer waiting time.4special order in the environment does not change, obtained with the classical M/M/2and M/M/1queueing model consistent results.