Modeling Fluctuations in the Quasi-static Approach Describing the Temporal Evolution of Retry Traffic

In previous work, we introduced the quasi-static retry traffic model, which describes the behavior of retry traffic generated by users who are impatient when waiting for a response from the system. In other words, the model describes interactions between users and the system. This interaction can be described in a simple form if it is assumed that the system offers infinitely fast (ideal) processing. Moreover, we proposed a performance evaluation technique called the quasi-static approach that replicates the temporal evaluation of traffic in finite speed (real-world) systems. In the quasi-static approach, the difference between the behavior of the ideal system and that of the real-world system is expressed as stochastic fluctuation. In this paper, we model the fluctuation for exactly replicating the behavior of retry traffic caused by user impatience using the quasi-static approach, and show the validity of an evaluation of the quasi-static approach by comparing the results of the quasi-static approach and that of conventional Monte Carlo simulation, in M/M/1and M/M/s-based systems with retry traffic. Key–Words: Retry traffic, Quasi-static approach, Fluctuations, Traffic model, Queueing system, Langevin equation, Fokker-Plank equation