The Analysis Of Queuing Systems With Negative Customers And Preemptive Priority

The queuing system with priority and negative customers has been weightily andwidely used in Communication Network, Electronic Countermeasures System, ComputerInterrupt System and Medical Treatment System, in recent years, it has been vitallyconcentrated by more and more scholars and has gradually developed into a new researchdirection. At present, the studies about this kind of queue model mostly focus on themodels with single-desk, but multi-server models are more common in our actualapplications. Therefore, to study the integrated mechanism with multi-server queuingsystem which contained priority and negative customers separately at the same time hasmore important theoretical significance and practical application value.In the article, a queuing system with priority and negative customers separately isresearched. Three different models are established and the numerical analysis of eachmodel is given respectively.Firstly, an M/M/1queuing system with two kinds of customers which has priority andnegative customers separately is investigated. By the analysis of the state transitiondiagram, the existing condition of steady-state equilibrium and the matrix-geometricsolution of the steady-state probability vectors are obtained. Then several performanceindicators are given. Further, the influence that parameters' variation brings toperformance indicators is observed through numerical calculation using MATLAB.Secondly, the M/M/m/k-m priority queuing system with negative customers isresearched. Through the analysis of state transition diagram, the steady-state equilibriumequations is set up and its matrix form is also given. By block matrix and matrix iterativemethod, the average queue length and the loss rate of the two classes are obtainedseparately. the influence that parameters' variation brings to performance indicators isinvestigated through numerical calculation by MATLAB.Finally, an M/M/m/k-m priority queuing system possessing customers who areclassified into positive and negative ones and arrive according to state is studied. Arrivingaccording to state is researched on the basis of the second model. By the analysis of the two kinds of the customers' average queue length, the delay time of the two kids ofcustomers in system can be estimated. The servers' service rate and the capacity of thewaiting track can be improved by the analysis of the overflow rate. Then the system canbe optimized and satisfies different needs. It has practical significance to the developmentof the communication networks.