Individual and Social Optimization in Birth-Death Congestion System with a General Cost-Benefit Structure.
Abstract
The authors consider optimal control of the arrival process to a stochastic congestion system modelled as a birth-death process, with arbitrary birth (arrival) and death (service) rates. An arriving customer who enters the system receives a net benefit which is decreasing in the number of customers already present. Control policies of a critical-number form are examined from the standpoint of individual optimization, social optimization, and facility optimization, with no discounting (average-return criterion). Previous results of Naor and Knudsen are generalized. In particular, the authors give a simple proof, in a more general setting, that fewer customers are admitted under social optimization than individual optimization. Sufficient conditions are given for the unimodality of the average-return function, and hence, for a local (social) optimum to be global. For the case of linear holding cost it is shown that the presence of congestion is appropriately characterized by an average-decreasing service rate, a weaker condition than concavity. Applications include certain traffic-flow and computer systems, as well as classical queueing systems.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 20, 1976
- Accession Number
- ADA033267
Entities
People
- Niels Chr. Knudsen
- Shaler Stidham Jr.
Organizations
- Stanford University