Telecommunications – Radiotelephone system – Zoned or cellular telephone system
Reexamination Certificate
1999-10-29
2002-05-28
Maung, Nay (Department: 2681)
Telecommunications
Radiotelephone system
Zoned or cellular telephone system
C455S067150, C455S067700
Reexamination Certificate
active
06397066
ABSTRACT:
FIELD OF THE INVENTION
The present invention relates generally to wireless communication systems and, more particularly, to a system and method for modeling and analyzing complex issues in a wireless communication system.
BACKGROUND OF THE INVENTION
The cellular industry has made phenomenal strides in commercial operations both in the United States and the rest of the world. Growth in major metropolitan areas has far exceeded expectations and is rapidly outstripping system capacity. If this trend continues, the effects of this industry's growth will soon reach even the smallest markets. Innovative solutions are required to meet these increasing capacity needs as well as to maintain high quality service and avoid rising prices.
In addition to the challenges posed by the need for greater system capacity, the designers of future wireless communication systems have their own unique set of challenges. For example, in order to engineer efficient wireless systems, designers need to be able to quickly and accurately estimate the capacity of a wireless communication system and analyze its performance.
Conventional approaches to capacity estimation and performance analysis involve the use of analytical formulae, computer simulations, or classical numerical methods. The use of analytical formulae, however, generally necessitates unrealistic assumptions (e.g., ignoring redialing or abandoning behavior of wireless customers when estimating the capacity of a wireless system). Similarly, the use of computer simulations typically requires a substantial setup time and achieves a less accurate estimate. In addition, the use of classical numerical methods generally requires an amount of computation time that makes use of such methods impractical.
A class of analytical models exists, called “multi-dimensional birth-death models,” that can be easily used to accurately model many capacity estimation and performance analysis issues. Unfortunately, the classical numerical approach to solving these models is well known as an excessively slow and frequently impractical approach for large systems.
FIG. 1
illustrates a general two-dimensional birth-death model
100
that can be used to model many capacity estimation and performance analysis issues. The two-dimensional birth-death model
100
includes several states
110
. Each state represents how something is: its configuration, attributes, condition, or information content. For example, a state may represent a specific number of voice calls and a specific number of data calls occupying a channel in a wireless system at a given instance.
As illustrated, a system may transition from a first state to any of its nearest neighboring states. For example, a system may transition from state
110
a
to its neighboring state to the west, its neighboring state to the south, its neighboring state to the east, its neighboring state to the southwest, or its neighboring state to the southeast.
A two-dimensional birth-death model, such as model
100
, can be used to analyze a variety of telecommunications issues, as well as other types of issues. For example, three areas of importance to designers of wireless systems that can be represented by two-dimensional birth-death models include analyzing wireless traffic in a system while taking into account the effects of redial traffic, analyzing wireless traffic in a system while taking into account the effects of handoff traffic, and analyzing the use of different priority schemes in a wireless system having both voice and data traffic.
Conventional approaches to estimating the capacity of a cell site, such as the use of analytical formulae, typically consider only the regular traffic at the cell site. Such approaches do not, however, take into account the effects of customers redialing in those situations when an original call to the cell site is blocked. In order to obtain a more accurate estimate of the capacity of the cell site, both regular traffic and redial traffic should be considered. A two-dimensional birth-death model may be used to estimate the capacity of a system having both types of traffic. One dimension of the model (e.g., the horizontal axis of the model
100
in
FIG. 1
) may be assigned to the number of channels in use in the cell site while the other dimension (e.g., the vertical axis of model
100
) may be assigned to the number of customers who have been blocked, but may redial. By taking redial traffic into account when estimating a cell site's capacity, a more accurate estimation may be obtained.
A two-dimensional birth-death model may also be used to analyze wireless traffic in a system while taking into account regular and handoff traffic. Typically, system designers treat both types of traffic the same in order to simplify system analyses. In order to increase customer satisfaction, however, regular traffic and handoff traffic should be treated differently. For example, from a customer satisfaction perspective, it is often better to block a customer attempting a new telephone call than to drop a customer in the middle of a telephone call. When analyzing such a system using a two-dimensional birth-death model, one dimension may be assigned to the number of new calls in the system and the other dimension to the number of hand-in calls. Such a model would allow system designers to analyze different types of reservation (or priority assignment) techniques.
Similarly, if a channel in a wireless system handles both voice and data traffic, it may be desirable to assign different levels of priority to the traffic types. A two-dimensional birth-death model could represent such a system. System designers could analyze the effects of the different levels of priority by assigning one dimension of the two-dimensional birth-death model to the number of voice calls in the system and the other dimension to the number of data calls in the system. As a result, a variety of priority schemes can be easily analyzed.
To analyze two-dimensional birth-death models, the steady state ergodic probability of a column vector being in the set of states ((j, 0), . . . , (j, n)) is defined as
e
j
=(e
j0
, . . . , e
jn
)
T
, where e
j0
is the probability of being in state (j, 0) and e
jn
is the probability of being in state (j, n), and the infinitesimal generator of the probability flow from (j, i) to (j−1, k) to be [&ngr;
j
−
]
i,k
, from (j, i) to (j+1, k) to be [&ngr;
j
+
]
i,k
, from (j, i) (j, k) to be [&ngr;
j
0
]
i,k
if i≠k and the total probability flow out of (j, i) to be −[&ngr;
j
0
]
i,i
, i.e., −[&ngr;
j
0
]
i,i
=&Sgr;
k
([&ngr;
j
+
]
i,k
+&khgr;
(i≠k)
[&ngr;
j
0
]
i,k
+[&ngr;
j
−
]
i,k
) so
(&ngr;
j
+
+&ngr;
j
0
+&ngr;
j
−)
1
=
0
(1)
where &ngr;
j
0
, &ngr;
j
0
, and &ngr;
j
−
, are matrices, and
1
and
0
are vectors consisting of only 1's and 0's, respectively.
Two-dimensional birth-death equations have a steady state solution satisfying
&khgr;
{j≠0}
e
j−1
T
&ngr;
j−1
+
+
e
j
t
&ngr;
j
0
+&khgr;
{j≠n}
e
j+1
T
&ngr;
j+1
−
=
0
j=0, . . . , m, (2)
and
∑
j
=
0
m
e
_
j
T
1
_
=
1.
(
3
)
In general, when the condition of the subscript associated with &khgr; is true, the value of &khgr; equals 1 and equals 0 otherwise. In equation 2, therefore,
X{j≠0}
equals 1 when j≠0 and equals 0 when j=0.
To simplify future notation, assume
&ngr;
0
−
=&ngr;
m
+
=0. (4)
where &ngr;
0
−
and &ngr;
m
+
are (m+1×m+1) matrices and 0 is a matrix consisting only of 0's. Note that equations (2) and (3) are the solution to equations
e
T
&ngr;=
0
and
e
T
1
=1
where
e
T
=(
e
0
T
,
e
1
T
, . . . ,
e
n
T
) is a 1×(n+1)(m+1) vector and
v
=
(
v
0
0
v
0
+
0
0
⋯
0
0
v
1
Maung Nay
Suchyta Leonard Charles
Trinh Sonny
Verizon Laboratories Inc.
Weixel James K.
LandOfFree
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