5.14 Interdistrict dispatching, revisited In Section
5.6 we found that for a nontimevarying system with _{n}(t) = _{n}, _{n}(t) = _{n}, the fraction of dispatches that
are interdistrict dispatches is
 Examine the special case _{n} = , and
physically interpret your result.
 Examine the special case _{n} constant, and physically
interpret your
result.
 In the text we developed (5.55), allowing for a timevarying
system in which the sector car is always given first
preference. However, for a system in which the dispatcher has car
location information, he may prefer to assign an outofsector car that
is closer to the scene than the sector car.
Our previous analysis can be generalized to allow for this
type of behavior. Let
a_{n}(t) =  probability that unit n is
assigned to a call that arrives from sector n at time t,
given that unit n is available

Derive the analogous result to (5.55) for this more general
model. What are the physical implications of the result?
 Does the practical significance of the results above change if
we allow a queue to form? As a guide to answering this
question, consider a nontimevarying system in nearsaturation
conditions (i.e., a queue almost always exists). A call
that arrives when all N servers are busy is entered in queue. The
queue is depleted in a firstcome, firstserved manner.
Prove that
