Geoscience Reference
In-Depth Information
2. Facilities contain resources (often called “servers”) that have
limited
capacity
and
stochastic service times
.
3. Customer-facility interactions happen as the result of
customers traveling to
facilities
to seek service, i.e., our primary focus is on the “fixed” or “immobile”
server models (in the “mobile server” case, servers travel to customers to provide
service).
4. Due to stochastic arrivals of customer demands at the facilities, stochastic service
times, and limited capacities, facilities may experience periods of
congestion
where not all arriving demands can be served immediately. Customers that arrive
when the system is busy may either enter a queue or leave without getting service.
This behavior will result in either
queues
,or
lost demands
, or both.
Applications of these models range from public service facilities such as hospitals,
medical clinics and government offices, to private facilities such as retail stores or
repair shops.
We note that assumptions listed above specifically exclude a number of interest-
ing and important classes of related location models (some of these are treated in
other chapters in the current volume). First, there are many models that incorporate
capacity limitations in a deterministic, rather than stochastic, manner. These include
models seeking to ensure that there is sufficient average capacity to provide
adequate service, models that try to design a system that should perform well
even under stochastic conditions by equalizing loads between facilities, and models
that handle possible congestion indirectly by requiring certain reserve capacity
at the facilities. All of these can be regarded as deterministic approximations of
the underlying stochastic system. While this deterministic approach leads to large
technical simplifications and, as a result, much easier computations, the roughness
of the approximation is usually impossible to estimate a priori. This may lead to
systems with poor levels of customer service (at some of the facilities), and is
typically not appropriate in cases where understanding and controlling potential
congestion is important.
Second, there are some models where facilities are modeled as reliability, rather
than queueing, systems, i.e., a facility may “fail” with certain probability in some
periods, at which point it cannot provide service to customers (who are typically
assumed to try to seek service from non-failed facilities). These models do incor-
porate stochastic demands explicitly. Moreover, “failure” periods may be regarded
as representing periods of congestion at the facilities when new customer arrivals
are blocked. Thus, these models are closer to the systems we study. However,
the key difference is that “reliability” models treat the blockage probability as
exogenous to the system (a typical assumption is that each facility may fail with
certain probability at any time, where such probability is a system parameter), while
models where facilities are represented as queues treat the probability of blockage as
endogenous, i.e., it is a direct outcome of other decisions such as capacity allocation
and customer-facility interactions. Thus, reliability models can only be regarded as
approximations for the systems we are interested in.
