Some servers are to be located at nodes of a network. Demand for services of these servers is located at each node and a subset of the nodes is to be chosen to locate one server in each. Each customer selects a server with a probability dependent on distance and a certain amount of benefit is achieved after giving service to the customer. Customers may waive receiving service with a known probability. The objective is to maximize the total benefit. In this paper, the problem is formulated, three solution algorithms are developed and applied to some numerical examples to analyze the results.

The main objective of facilities location and service system design is covering of potential customers’ demand. Many location models are extended with the covering objective and considered constraints, details of problem and its different aspects. In this paper the maximal covering location-allocation model for Congested system is extended in the competitive environment. In the proposed model, several important characteristics such as spatial interaction model, congestion, the competitive user-choice environment and probabilistic demand are considered. The objective of the model is maximization of the demand captured by each facility in the competitive environment. The optimization software of lingo 8 and the genetic algorithm are used for solving the small-size problems. Due to the complexity of problem and its nonlinear nature, the software of lingo 8 cant solved the large-size problems and the genetic algorithm is applied to solve the larger size problems. Numerical results verify the effectiveness of proposed algorithm for solving the model and show that the use of queuing theory in service system design can improve different service strategies, promote organization’s business process and increase customer’s satisfaction.

There exist various service systems that have hierarchical structure. In hierarchical service networks, facilities at different levels provide different types of services. For example, in health care systems, general centers provide low-level services such as primary health care services, while the specialized hospitals provide high-level services. Because of demand congestion in service networks, location of servers and allocation of demand nodes have a strong impact on the length of queues at servers as well as on the response times to service calls. The thrust of this article is the development of hierarchical location-allocation models for Congested systems by employing queueing theory in a fuzzy framework. The new models allow partial coverage of demand nodes and approximate determination of parameters. Using queueing theory and fuzzy conditions, both referral and nested hierarchical models are developed for the maximal covering location problem (MCLP). An example is solved for both an existing probabilistic model and the new fuzzy models and the results are compared.

A fuzzy queuing coherent hierarchical location-allocation model is developed for Congested systems. The parameters of the model are approximately evaluated and stated as fuzzy-numbers. The coverage of demand nodes is also considered in an approximate manner and is stated by the degree of membership. Using the queuing theory and fuzzy conditions, a coherent hierarchical model is developed for the Maximal Covering Location Problem (MCLP). An example problem is solved and presented, along with results. Conclusions and future extensions are also included.    

Queue length is one of the fundamental parameters of traffic flow on arterial streets that is the performance and flow optimization criteria However this measure of arterials less attention and has been investigated. This could be caused by periodic disruption on traffic flow by signal lights that make difficult evaluation of traffic flow on arterials. On the other hand the problem gets even more difficult when signal links are Congested. In this paper, queue length on Congested arterials is considered as one of the fundamental traffic parameters.