Abstract: We consider an M/M/1 queueing system in which the queue length may or may not be observable by a customer upon entering the system, and compare the observable and unobservable models with respect to system properties and performance measures under two different types of optimal customer behaviour, referred to as selfishly optimal and socially optimal. We show that under both types of optimal customer behaviour, the equality of effective queue-joining rates between the observable and unobservable systems results in differences with respect to other performance measures such as mean busy periods and waiting times. We also show that the equality of selfishly optimal queue-joining rates between the two types of system precludes the equality of socially optimal joining rates, and vice versa.
@article{shone2013comparisons,
title = {Comparisons between observable and unobservable {M/M/1} queues
with respect to optimal customer behavior},
author = {Shone, Rob and Knight, Vincent A. and Williams, Janet E.},
journal = {European Journal of Operational Research},
volume = {227},
number = {1},
pages = {133--141},
year = {2013},
doi = {10.1016/j.ejor.2012.12.016},
}