MAXIMUM-LIKELIHOOD ESTIMATES FOR QUEUES WITH STATE-DEPENDENT SERVICE,

Abstract

Methods are indicated for the maximum-likelihood estimation of the arrival and service parameters of ergodic queueing processes with service times whose distributions are state dependent. Two basic methods of sampling are considered. For the first, only the queue size at each departure point is observed, while for the second, the time between successive departures and the lengths of the idle periods are noted along with the queue size. Based upon each sampling method, procedures are developed for deriving estimates both when the effect of initial queue size on the likelihood function is ignored and when it cannot be. Three specific models of this semi-Markov process are presented, along with a numerical example illustrating some of the results, based on data generated by simulating a known model. (Author)

Document Details

Document Type
Technical Report
Publication Date
Mar 24, 1970
Accession Number
AD0704788

Entities

People

  • Carl M. Harris
  • Tarsaim L. Goyal

Organizations

  • George Washington University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Collecting Methods
  • Markov Processes
  • Mathematical Analysis
  • Mathematics
  • Maximum Likelihood Estimation
  • Sampling

Fields of Study

  • Mathematics

Readers

  • Computational Modeling and Simulation
  • Mathematical Modeling and Probability Theory.