Parameter Estimation of <inline-formula> <tex-math notation="LaTeX">$M_{t}/M/1/K$ </tex-math></inline-formula> Queueing Systems With Utilization Data

• Main Authors: Chen Li, Hiroyuki Okamura, Tadashi Dohi
• Format: Article
• Language: English
• Published: IEEE 2019-01-01
• Series: IEEE Access
• Subjects: Queueing systems; time intervals; utilization data; EM algorithm
• Online Access: https://ieeexplore.ieee.org/document/8672563/
• ISSN: 2169-3536

Utilization data are defined as the time series data consisting of time fractions of busy periods in fixed time intervals and are practically used to represent server conditions, such as CPU utilization. In general, it is more challenging to estimate the model parameters from the utilization data since we do not know the exact job arrival time and the service time from the utilization data. In this paper, we consider an approach to estimate the model parameters from the utilization data by assuming a few model assumptions. In particular, we suppose an M_t/M/1/K queueing system whose job arrival follows a Non-homogeneous Poisson Process (NHPP) and propose a parameter estimation method for the NHPP approximately from the utilization data based on the maximum likelihood estimation (MLE) via the expectation maximization (EM) algorithm. In numerical experiments, we generate the simulated utilization data of an M_t/M/1/K queueing system and investigate the effectiveness of our method. Also, we use the real CPU utilization data to exhibit the performance evaluation.