## Abstract

This work presents a strategic observable model where customer heterogeneity is induced by the customers’ locations and travel costs. The arrival of customers with distances less than x is assumed to be Poisson with rate equal to the integral from 0 to x, of a nonnegative intensity function h. In a loss system M/G/1/1 we define the threshold Nash equilibrium strategy x_{e} and the socially-optimal threshold strategy x*. We investigate the dependence of the price of anarchy (PoA) on the parameter x_{e} and the intensity function. For example, if the potential arrival rate is bounded then PoA is bounded and converges to 1 when x_{e} goes to infinity. On the other hand, if the potential arrival rate is unbounded, we prove that x*/x_{e} always goes to 0, when x_{e} goes to infinity and yet, in some cases PoA is bounded and even converges to 1; if h converges to a positive constant then PoA converges to 2; if h increases then the limit of PoA is at least 2, whereas if h decreases then PoA is bounded and the limit of PoA is at most 2. In a system with a queue we prove that PoA may be unbounded already in the simplest case of uniform arrival.

Original language | English |
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Pages (from-to) | 580-588 |

Number of pages | 9 |

Journal | European Journal of Operational Research |

Volume | 265 |

Issue number | 2 |

DOIs | |

State | Published - 1 Mar 2018 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2017 Elsevier B.V.

## Keywords

- Observable queue
- Price of anarchy
- Profit maximization
- Queuing
- Travel costs