On the approximation of empirical data for service system simulations

Abstract

The difficulties associated with parameter estimation for phase-type approximations of empirical data distributions in queue modelling are well known. While significant progress has been achieved in improving such approximations, difficulties in parameter estimation still limit the extent to which queue modelling is applied in practice. This paper presents a simplified technique for approximating empirical data in service system simulations, based on the specialised Cox phase-type distribution. When utilised in simulation modelling of a service system, the specialised Cox distribution is shown to provide improved approximations to the combined waiting and service time distribution without the need for complex parameter estimation techniques. This approach should enable much greater flexibility in the application of queue modelling to service systems.

Keywords:

• queueing models
• simulation
• Cox distributions
• parameter estimation
• hospitals

Notes

1 For a mathematical treatment of the Poisson process, see for example Bolch et al (2006).

2 The analysis of Markov processes is outside the scope of this paper. Interested readers may wish to consult, for example, Cox and Miller (1965) or Bolch et al (2006).

3 Further information on these methods is available, for example, in Rice (1995).

4 The interpretation of the notation is ‘smallest integer greater than x’.

5 Model representation using Kendall's Notation, with H₂ representing the two-phase mixed exponential service time distribution. Similar representations are provided for the other models.