### Abstract

The classic optimal transportation problem consists in finding the most cost-effective way of moving masses from one set of locations to another, minimizing its transportation cost. The formulation of this problem and its solution have been useful to understand various mathematical, economical, and control theory phenomena, such as, e.g., Witsenhausen's counterexample in stochastic control theory, the principal-agent problem in microeconomic theory, location and planning problems, etc. In this work, we incorporate the effect of network congestion to the optimal transportation problem and we are able to find a closed form expression for its solution. As an application of our work, we focus on the mobile association problem in cellular networks (the determination of the cells corresponding to each base station). In the continuum setting, this problem corresponds to the determination of the locations at which mobile terminals prefer to connect (by also considering the congestion they generate) to a given base station rather than to other base stations. Two types of problems have been addressed: a global optimization problem for minimizing the total power needed by the mobile terminals over the whole network (global optimum), and a user optimization problem, in which each mobile terminal chooses to which base station to connect in order to minimize its own cost (user equilibrium). This work combines optimal transportation with strategic decision making to characterize both solutions.

Original language | English (US) |
---|---|

Article number | 6471755 |

Pages (from-to) | 2018-2031 |

Number of pages | 14 |

Journal | IEEE Transactions on Automatic Control |

Volume | 58 |

Issue number | 8 |

DOIs | |

State | Published - Aug 5 2013 |

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### Keywords

- Base stations
- Cellular networks
- Mobile communication
- Network topology
- Resource management
- Signal-to-noise ratio (SNR)
- Throughput

### ASJC Scopus subject areas

- Control and Systems Engineering
- Computer Science Applications
- Electrical and Electronic Engineering

### Cite this

*IEEE Transactions on Automatic Control*,

*58*(8), 2018-2031. [6471755]. https://doi.org/10.1109/TAC.2013.2250072

**Optimum and equilibrium in assignment problems with congestion : Mobile terminals association to base stations.** / Silva, Alonso; Hamidou, Tembine; Altman, Eitan; Debbah, Mérouane.

Research output: Contribution to journal › Article

*IEEE Transactions on Automatic Control*, vol. 58, no. 8, 6471755, pp. 2018-2031. https://doi.org/10.1109/TAC.2013.2250072

}

TY - JOUR

T1 - Optimum and equilibrium in assignment problems with congestion

T2 - Mobile terminals association to base stations

AU - Silva, Alonso

AU - Hamidou, Tembine

AU - Altman, Eitan

AU - Debbah, Mérouane

PY - 2013/8/5

Y1 - 2013/8/5

N2 - The classic optimal transportation problem consists in finding the most cost-effective way of moving masses from one set of locations to another, minimizing its transportation cost. The formulation of this problem and its solution have been useful to understand various mathematical, economical, and control theory phenomena, such as, e.g., Witsenhausen's counterexample in stochastic control theory, the principal-agent problem in microeconomic theory, location and planning problems, etc. In this work, we incorporate the effect of network congestion to the optimal transportation problem and we are able to find a closed form expression for its solution. As an application of our work, we focus on the mobile association problem in cellular networks (the determination of the cells corresponding to each base station). In the continuum setting, this problem corresponds to the determination of the locations at which mobile terminals prefer to connect (by also considering the congestion they generate) to a given base station rather than to other base stations. Two types of problems have been addressed: a global optimization problem for minimizing the total power needed by the mobile terminals over the whole network (global optimum), and a user optimization problem, in which each mobile terminal chooses to which base station to connect in order to minimize its own cost (user equilibrium). This work combines optimal transportation with strategic decision making to characterize both solutions.

AB - The classic optimal transportation problem consists in finding the most cost-effective way of moving masses from one set of locations to another, minimizing its transportation cost. The formulation of this problem and its solution have been useful to understand various mathematical, economical, and control theory phenomena, such as, e.g., Witsenhausen's counterexample in stochastic control theory, the principal-agent problem in microeconomic theory, location and planning problems, etc. In this work, we incorporate the effect of network congestion to the optimal transportation problem and we are able to find a closed form expression for its solution. As an application of our work, we focus on the mobile association problem in cellular networks (the determination of the cells corresponding to each base station). In the continuum setting, this problem corresponds to the determination of the locations at which mobile terminals prefer to connect (by also considering the congestion they generate) to a given base station rather than to other base stations. Two types of problems have been addressed: a global optimization problem for minimizing the total power needed by the mobile terminals over the whole network (global optimum), and a user optimization problem, in which each mobile terminal chooses to which base station to connect in order to minimize its own cost (user equilibrium). This work combines optimal transportation with strategic decision making to characterize both solutions.

KW - Base stations

KW - Cellular networks

KW - Mobile communication

KW - Network topology

KW - Resource management

KW - Signal-to-noise ratio (SNR)

KW - Throughput

UR - http://www.scopus.com/inward/record.url?scp=84880874221&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84880874221&partnerID=8YFLogxK

U2 - 10.1109/TAC.2013.2250072

DO - 10.1109/TAC.2013.2250072

M3 - Article

AN - SCOPUS:84880874221

VL - 58

SP - 2018

EP - 2031

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

IS - 8

M1 - 6471755

ER -