Planning wireless networks by shortest path

Abstract

Transmitters and receivers are the basic elements of wireless networks and are characterized by a number of radio-electrical parameters. The generic planning problem consists in establishing suitable values for these parameters so as to optimize some network performance indicator. The version here addressed, namely the Power Assignment Problem (pap), is the problem of assigning transmission powers to the transmitters of a wireless network so as to maximize the satisfied demand. This problem has relevant practical applications both in radio-broadcasting and in mobile telephony. Typical solution approaches make use of mixed integer linear programs with huge coefficients in the constraint matrix yielding numerical inaccuracy and poor bounds and cannot be exploited to solve large instances of practical interest. In order to overcome these inconveniences, we developed a two-phase heuristic to solve large instances of pap , namely a constructive heuristic followed by an improving local search. Both phases are based on successive shortest path computations on suitable directed graphs. Computational tests on a number of instances arising in the design of the Italian Digital Video Broadcasting are presented.Keywords: wireless network optimization, mixed integer programs, exponential neighborhood search. * Partially supported by MIUR, Project 2006015972, Optimization models and algorithms for the design of wireless networks.

GUB Covers and Power-Indexed Formulations for Wireless Network Design

“…the SIR inequalities of testpoints recognized as covered are actually unsatisfied (similar problems were also reported in Kalvenes et al (2006), Kennington et al (2010) and Mannino et al (2009)). We detect such coverage errors by evaluating the solutions offline: after the optimization process, we verify that the SIR inequality corresponding to Article published in Management Science each nominally covered testpoint is really satisfied by the power vector of the returned solution.…”

Network Optimization

“…Or, alternatively, if its best server is "stronger" than its strongest interferer. In [8] the authors show that, in most cases of practical interest, this is indeed a good approximation of the original SIR constraint. By assuming p b ∈ [ε, P b ], with ε > 0 very small, and by taking the logarithm 2 of both left and right hand side multiplied by 10, the system Σ ′ can be rewritten as:…”

“…The resulting MILP presents severe drawbacks, highlighted in several works, e.g. [5,7,8]. First, the coefficients in the SIR inequalities may vary over a very wide range, with differences up to 10 12 or even larger.…”

“…To this end, we proceed in a similar way to [8]. Namely, we generate a new system Σ ′ obtained from Σ by substituting each (1) with the system:…”

Negative Cycle Separation in Wireless Network Design

“…[5,7,8]. First, the coefficients in the SIR inequalities may vary over a very wide range, with differences up to 10 12 or even larger.…”