M/C-2/c/K queuing model and optimization for a geriatric care center


Kocer U. U. , Ozkar S.

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, cilt.31, ss.892-911, 2015 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 31 Konu: 6
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1002/asmb.2119
  • Dergi Adı: APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY
  • Sayfa Sayıları: ss.892-911

Özet

Queuing systems with finite buffers are reasonable models for many manufacturing, telecommunication, and healthcare systems. Although some approximations exist, the exact analysis of multi-server and finite-buffer queues with general service time distribution is unknown. However, the phase-type assumption for service time is a frequently used approach. Because the Cox distribution, a kind of phase-type distribution, provides a good representation of data with great variability, it has a vast area of application in modeling service times.

Queuing systems with finite buffers are reasonable models for many manufacturing, telecommunication, and healthcare systems. Although some approximations exist, the exact analysis of multi-server and finite-buffer queueswith general service time distribution is unknown. However, the phase-type assumption for service time is a frequently used approach. Because the Cox distribution, a kind of phase-type distribution, provides a good representation of data with great variability, it has a vast area of application in modeling service times.
The research focus is twofold. First, a theoretical structure of a multi-server and finite-buffer queuing system in which the service time is modeled by the two-phase Cox distribution is studied. It is focused on finding an efficient solution to the stationary probabilities using the matrix-geometric method. It is shown that the stationary probability vector can be obtained with the matrix-geometric method by using level-dependent rate matrices, and the mean queue length is computed. Second, an empirical analysis of the model is presented. The proposed methodology is applied in a case study concerning the geriatric patients. Some numerical calculations and optimizations are performed by using geriatric data.