A queueing analysis of max-min fairness, proportional fairness and balanced fairness

Abstract

We compare the performance of three usual allocations, namely max-min fairness, proportional fairness and balanced fairness, in a communication network whose resources are shared by a random number of data flows. The model consists of a network of processorsharing queues. The vector of service rates, which is constrained by some compact, convex capacity set representing the network resources, is a function of the number of customers in each queue. This function determines the way network resources are allocated. We show that this model is representative of a rich class of wired and wireless networks. We give in this general framework the stability condition of max-min fairness, proportional fairness and balanced fairness and compare their performance on a number of toy networks.

Inequity averse optimization in operational research

“…Applications include bandwidth or channel allocation (Tomaszewski, 2005;Lee et al, 2004;Lee & Cho, 2007;Luss, 2008;Salles & Barria, 2008;Ogryczak et al, 2008;Luss, 2010;Luss, 2012a;Jeong et al, 2005;Chang et al, 2006;Zukerman et al, 2008;Morell et al, 2008;Zhang & Ansari, 2010;Bonald et al, 2006;Heikkinen, 2004;Ogryczak et al, 2005;Kunqi et al, 2007), water rights allocation (Udías et al, 2012), health care planning (Earnshaw et al, 2007;Demirci et al, 2012;Hooker & Williams, 2012;Bertsimas et al, 2013), WIP (Kanban) allocation in production systems (Ryan & Vorasayan, 2005), fixed cost allocation (Li et al, 2013;Butler & Williams, 2006), and public resource allocation such as allocating voting machines to election precincts . There are also studies that consider general resource allocation settings such as Bertsimas et al (2011), Hooker (2010, Nace and Orlin (2007), Medernach and Sanlaville (2012) and Bertsimas et al (2014).…”

“…Bertsimas et al (2014) propose a modeling framework for general dynamic resource allocation Table 2 Classical problems in OR re-considered with equity concerns. Tomaszewski (2005), Lee, Moon, and Cho (2004), Lee and Cho (2007), Luss (2008), Salles and Barria (2008), Ogryczak, Wierzbicki, and Milewski (2008), Luss (2010), Luss (2012a), Jeong, Kim, and Lee (2005), Chang, Lee, and Kim (2006), Zukerman, Mammadov, Tan, Ouveysi, and Andrew (2008), Morell, Seco-Granados, and Vázquez-Castro (2008), Zhang and Ansari (2010), Bonald, Massoulié, Proutière, andVirtamo (2006), Heikkinen (2004), Ogryczak, Pioro, and Tomaszewski (2005), Udías, Ríos Insua, Cano, and Fellag (2012), Earnshaw, Hicks, Richter, and Honeycutt (2007), Demirci, Schaefer, Romeijn, and Roberts (2012), Hooker and Williams (2012), Bertsimas, Farias, and Trichakis (2013), Ryan and Vorasayan (2005), Li, Yang, Chen, Dai, and Liang (2013), Butler and Williams (2006), Yang, Allen, Fry, and Kelton (2013), Trichakis (2011), Bertsimas, Farias, andTrichakis (2012), Hooker (2010), Nace and Orlin (2007), Medernach and Sanlaville (2012), Bertsimas, Gupta, and Lulli (2014), Karsu and Morton (2014), Johnson, Turcotte, and Sullivan (2010), Kozanidis (2009), Eiselt and Marianov (2008), Vossen and Ball (2006), …”

“…As the arrival time and/or the service requirement level of a customer are used as a basis for claim in the server allocation we discuss these measures in the balance section. Bonald et al (2006) model a communication network problem, where the network is represented as a network of processor-sharing queues and analyze different fairness schemes.…”

Interacting queues with server selection and coordinated scheduling—application to cellular data networks

“…For any κ > 0, it has been shown in Bonald et al (2006) that the κ-fair scheduler achieves stability whenever possible.…”

Limit Theorems for Markovian Bandwidth-Sharing Networks with Rate Constraints

“…In some cases, it is even possible to derive necessary and sufficient conditions for steady-state distributions of this type to exist. This work is well summarized in Bonald et al (2006).…”