The GI/M/1 Queue with Controlled Arrivals.

Abstract

A GI/M/1 queue is studied, in which the arrival process can be controlled by accepting or rejecting arriving customers or changing a toll. An entering customer receives a (random) reward and there is a holding cost, which is convex in the number of customers present. Socially and individually optimal joining policies are compared for finite and infinite horizons, with and without discounting. A socially optimal policy is shown to be less likely to accept a customer than an individually optimal policy, and both policies are less likely to accept as the number of customers present increases, the horizon length increases, or the discount rate decreases. The properties of optimal congestion tolls are examined and it is discovered that the toll is monotonic when either the horizon is finite or the discount rate is positive, whereas it can be monotonic for infinite-horizon, average-return problems. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jul 21, 1977
Accession Number
ADA044981

Entities

People

  • Shaler Stidham Jr.

Organizations

  • Stanford University

Tags

Communities of Interest

  • Human Systems

DTIC Thesaurus Topics

  • Computations
  • Congestion
  • Equations
  • Markov Chains
  • Military Research
  • Operations Research
  • Probability
  • Queueing Theory
  • Random Variables
  • Sequences
  • Stationary
  • Steady State
  • Supply Chain Management
  • Terminals
  • Theorems
  • United States
  • United States Government

Readers

  • Mathematical Modeling and Probability Theory.
  • Organizational Psychology.