The Simulation Of Queueing Systems With Loss And Impatient Customers

In this paper we mainly study the queueing systems with lost and impatient customersunder the condition of heavy-traffic and do some analog simulations, including single-serverqueues and multi-server queues.For the single-server queue system G/G/1/k with lost customers, we design thesimulation algorithm. Take M/M/1/k for example, we use matlab to simulate and analysisthe relationship between the loss proportions and waiting room and service intensity. For themulti-server queue system G/GI/m/k with lost customers, only considering the situationthat the arrival from single source，we establish the queueing model and scale stochasticprocess, apply the continuous-mapping approach and functional central limit theorem(FCLT)to obtain the heavy-traffic stochastic-process limit for the queue-length process and lossprocess, we also give a conclusion that the loss proportions weak converge to a determinevalue. Take M/M/m/k for example, we also use matlab to simulate and analysis therelationship between the loss proportions and waiting room and services.For the single-server queue system with two-class customers, the arrival processes areindependent of each other and generally arrival. The first class customers have priority andthe second class customers become impatient because of the first class customers’ arrival. The“patience time” and the two class customers’ service times are both general distributions andthe service discipline is preemptive priority service. We design the simulation algorithm byestablishing the queueing model and defining the stochastic process. Under the condition ofheavy traffic, we use matlab to simulate and provide a new method to deal with such queueingproblems. On the basis of single-server queue system, we study the multi-server queue systemwith two-class customers, use matlab to simulate and analysis the relationship between theloss ratio and arrival rate and services.