Queueing Models With Stable Levy Motion In Heavy-traffic

In this paper the queueing models with Levy motion in heavy traffic are mainly studied.If interarrival times and service times belong to heavy-tailed distribution, Brownian motion isnot suitable for these queueing models. Heavy-tailed distribution is different from normaldistribution and variates have finite mean, infinite variance. It is necessary to study somestochastic-process limits of queueing models with Levy motion.First of all, the paper has studied the queueing models with infinite waiting room,thesemodels include simple-server queueing model, multiserver queueing model and multiplechannels model. The aims are heavy-traffic stochastic-process limits for queue-length andwaiting times processes of queueing models with heavy-tailed distribution. As a result, thesestochastic-process limits convergence to stable Levy motion by FCLT and continuousmapping theorem.And then, the study of the queueing models with finite waiting room like as the infinitewaiting rooms queueing models, the result shows that queue-length processes convergence tostable Levy motion. At same time, the paper is also studied the loss process and the loss rateof different servers.At last, this paper simulates these queueing models and plot the pictures.From thesepictures,it can be seen that processes have some unmatched jumps. The processes are Levymotions with finite mean and infinite variance.