When dealing with the design of service networks, such as health and emergency medical services, banking or distributed ticket-selling services, the location of service centers has a strong influence on the congestion at each of them, and, consequently, on the quality of service. In this paper, several probabilistic maximal covering locationallocation models with constrained waiting time for queue length are presented to consider service congestion. The first model considers the location of a given number of single-server centers such that the maximum population is served within a standard distance, and nobody stands in line for longer than a given time or with more than a predetermined number of other users. Several maximal coverage models are then formulated with one or more servers per service center. A new heuristic is developed to solve the models and tested in a 30-node network.

We o er a formulation that locates hubs on a network in a competitive e nvironment that is, customer capture is sought, which happens whenever the location of a new hub results in a reduction of the current cost (time, distance) needed by the tra c that goes from the speci ed origin to the speci ed destination. The formulation presented here reduces the number of variables and constraints as compared to existing covering models. This model is suited for both air passenger and cargo transportation. In this model, each origindestination ow can go through either one or two h ubs, and each demand point can be assigned to more than a hub, depending on the di erent destinations of its tra c. Links (\spokes" have no capacity limit. Computational experience is provided.

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In this paper a p-median-like model is formulated to address the issue of locating new facilities when there is uncertainty. S e v eral possible future scenarios with respect to demand and/or the travel times/distance parameters are presented. The planner will want a strategy of positioning that will do as "well as possible" over the future scenarios. This paper presents a discrete location model formulation to address this P-Median problem under uncertainty. The model is applied to the location of re stations in Barcelona

Models are presented for the optimal location of hubs in airline networks, that take into consideration the congestion effects. Hubs, which are the most congested airports, are modeled as M/D/c queuing systems, that is, Poisson arrivals, deterministic service time, and c servers. A formula is derived for the probability of a number of customers in the system, which is later used to propose a probabilistic constraint. This constraint limits the probability of b airplanes in queue, to be lesser than a value α. Due to the computational complexity of the formulation, The model is solved using a meta-heuristic based on tabu search. Computational experience is presented.