| Article ID: | iaor20083619 |
| Country: | Japan |
| Volume: | 50 |
| Issue: | 1 |
| Start Page Number: | 1 |
| End Page Number: | 14 |
| Publication Date: | Dec 2007 |
| Journal: | Transactions of the Operations Research Society of Japan |
| Authors: | Nakade Koichi, Sugihara Hiroaki |
| Keywords: | facilities, public service, queues: applications |
In this paper, we analyze a facility location model in which a facility with shorter expected required time is utilized. Required time for facility consists of the round-trip travel time and the sojourn time, and each facility has a single server with exponentially distributed service time. An area in which customers live is divided in a form of meshes. Demand from each mesh forms a Poisson process. Customers first visit the nearer facility, but if one facility is congested, a part of customers who visited the facility will go to another facility. Then in a steady state each customer visits a facility with shorter expected required time, and the area is divided into two stable regions. The two-facility location model with the stable regions is formulated by using queueing theory, and a computation method for deriving a boundary line dividing these regions is proposed. From this boundary, overall expected required time and required time distributions for all customers can be derived. Properties of the stable regions are discussed by numerical examples.