This preview shows page 1. Sign up to view the full content.
Unformatted text preview: equilibrium, so EZn stays bounded, and hence Zn /n ! 0. The details
of completing this proof are too complicated to give here. However, in Example
3.6 we will give a simple proof of this. 107 3.2. APPLICATIONS TO QUEUEING THEORY 3.2.2 Cost equations In this subsection we will prove some general results about the GI/G/1 queue
that come from very simple arguments. Let Xs be the number of customers in
the system at time s. Let L be the long-run average number of customers in
L = lim
t!1 t 0
Let W be the long-run average amount of time a customer spends in the system:
W = lim
m=1 where Wm is the amount of time the mth arriving customer spends in the
system. Finally, let a be the long-run average rate at which arriving customers
join the system, that is,
a = lim Na (t)/t
t!1 where Na (t) is the number of customers who arrive before time t and enter the
system. Ignoring the problem of proving the existence of these limits, we can
assert that these quantities are rel...
View Full Document
This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).
- Spring '10
- The Land