A new optimal cost model of queue systems with Heavy-Tailed distribution

The heavy-tailed characteristic has been emerged in the distributions of Internet flow sizes, web pages and computer files. So the M/Heavy-Tailed/K queue system is the highlight of the research of queue systems. In this paper, it is firstly proved that the efficiency of multiple servers is equal to the single server when all of servers work with full load. Then, with the cost objective function, the optimal number of servers for the queue systems is presented with three heavy tailed distributions, which are the bimodal distribution, bounded Pareto distribution and power-law distribution. An event-driven simulator for queuing systems is proposed to the simulation of the M/HT/K queue systems. According to theoretical analysis and numerical simulation, the optimal number of servers for the M/HT/K system with cost objective function is less than that of system with the average response time as its objective function. It implies that the latter model emphasizes the optimization of the response time, not the optimal cost which is the key of the former system.