A Queuing System With Variable Service Rates

This paper studies a queuing model with variable service rates for M/M/n multiple service windows,which improves the queuing efficiency by changing the service rate.The first two chapters of this article introduced the background,development history,and basic knowledge of queuing theory.By studying the simple variable service for M/M/1 rate queuing model,and then increasing the service window,based on the variable service rate and queuing model for M/M/3?M/M/4,according to the classification of the service rate is divided into fast and slow changes and incremental changes.For these two methods,first construct a variable service rate queuing system model and the stable distribution of the queuing system,determine its birth and death process,then draw its state transition diagram of the queuing system,and list the equilibrium equation of each position in turn,The flexible use of the equations in the equilibrium state K,iterate each other,find the system idle probability p₀,and the target parameters of the queuing system.In the queuing system of this paper,if the service rate is the same,the conclusions obtained are consistent with the conclusions in the literature,and the correctness of the conclusions of the paper can be reflected from the side.In order to reflect the queuing system more objectively and truthfully,this paper finally uses two specific queuing examples to find the various data indicators of the examples,which reflects more real.