Geoscience Reference
In-Depth Information
Chapter 17
Stochastic Location Models with Congestion
Oded Berman and Dmitry Krass
Abstract
In this chapter we describe facility location models where consumers
generate streams of stochastic demands for service, and service times are stochastic.
This combination leads to congestion, where some of the arriving demands cannot
be served immediately and must either wait in queue or be lost to the system.
These models have applications that range from emergency service systems (fire,
ambulance, police) to networks of public and private facilities. One key issue is
whether customers travel to facilities to obtain service, or mobile servers travel to
customer locations (e.g., in case of police cars). For the most part, we focus on
models with static (fixed) servers, as the underlying queueing systems are more
tractable and thus a richer set of analytical results is available. After describing the
main components of the system (customers, facilities, and the objective function),
we focus on the customer-facility interaction, developing a classification of models
based on the how customer demand is allocated to facilities and whether the demand
is elastic or not. We use our description of system components and customer-
response classification to organize the rich variety of models considered in the
literature into four thematic groups that share common assumptions and structural
properties. For each group we review the solution approaches and outline the main
difficulties. We conclude with a review of some important open problems.
Keywords
Congestion
Facility location
Mobile and immobile servers
Queuing Stochastic demand
17.1
Introduction
The class of facility location models that is the main focus of the current chapter
make the following key assumptions:
1. Customers generate
stochastic
stream of demands, typically assumed to be a
Poisson process, or, more generally a renewal process.
