2024/12/09 by Hayashi, Kaito, Inoue, Yoshiaki, Takine, Tetsuya · 1 citation
#60J22 #60J27 #60K25 #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2412.06452
We consider queueing models, where customers arrive according to a continuous-time binomial process on a finite interval. In this arrival process, a total of K customers arrive in the finite time interval [0,T], where arrival times of those K customers are independent and identically distributed according to an absolutely continuous distribution defined by its probability density function f(t) on (0,T]. To analyze the time-dependent queue length distribution of this model, we introduce the auxiliary model with non-homogeneous Poisson arrivals and show that the time-dependent queue length distribution in the original model is given in terms of the time-dependent joint distribution of the numbers of arrivals and departures in the auxiliary model. Next, we consider a numerical procedure for computing the time-dependent queue length distribution in Markovian models with piecewise constant f(t). A particular feature of our computational procedure is that the truncation error bound can be set as the input. Some numerical examples are also provided.