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Performance analysis of microcellization for supporting two mobility classes in cellular wireless networks

01 Mar 2000-IEEE Transactions on Vehicular Technology (IEEE)-Vol. 49, Iss: 2, pp 321-333
TL;DR: An approximate analysis for computing the slow and fast call blocking probabilities in such a system and simple, but accurate approximations are developed for analyzing the isolated macrocell and its associated microcells.
Abstract: We study the call blocking performance obtained by microcellizing a macrocell network. Each macrocell is partitioned into microcells, and some of the channels originally allocated to the macrocell are assigned to the microlayer cells according to a reuse pattern. The arriving calls are classified as fast or slow; fast calls are always assigned only to macrocell channels, whereas for slow calls a microcell channel is first sought. Slow calls may be allowed to overflow to the macrolayer, but may be repacked to vacated microcell channels. Calls can change their mobility class during a conversation. We develop an approximate analysis for computing the slow and fast call blocking probabilities in such a system. We adopt the technique of analyzing an isolated macrocell with the Poisson arrival assumption and then iterating on the stationary analysis of the isolated macrocell to obtain stationary results for the multicell system. Simple, but accurate approximations are developed for analyzing the isolated macrocell and its associated microcells. The analyses based on the approximate isolated cell model are validated against simulations of a multicell model.

Summary (2 min read)

Introduction

  • Thus, the signaling capacity of the signaling processors (in the base stations and the mobile switching centers) can limit the call handling capacity of a cellular system as the cell size is decreased.
  • The scenario that the authors are concerned with is that there is a macrocellular network, with a given frequency allocation to each cell.
  • This aspect is also included in their model by allowing calls to undergomobility change; i.e., a fast call can become a slow call and vice versa.
  • In Section IV, the authors provide numerical results that show how accurate the analysis is in comparison with simulations of the model.

A. Handovers, Repacking, and Signaling

  • The authors define a handoff (or handover) as any event that causes the system to seek a new channel for an existing call in the system.
  • If this attempt fails, the call is not retained in the microlayer, but is dropped.
  • Handovers are also caused by the repacking of slow calls occupying macrolayer channels; i.e., slow calls that are assigned channels in the macrolayer are moved back to the microlayer on availability of channels in their respective microcells.
  • This increases the capacity of the system, but additional signaling will be incurred due to the channel reassignments.
  • The set of events that contribute to the signaling traffic are new call arrivals, cell boundary crossings, mobility changes, and repacking.

B. Model Parameters and Notation

  • New call arrival processes for the various macrocells are independent Poisson processes.
  • Furthermore, the intervals at which a mobile changes its mobility are also assumed to be exponentially distributed.
  • The microcells in the th macrocell are numbered using double indexes .
  • Probability that a call leaving macrocell enters macrocell ; probability that a call leaving microcell enters microcell, also known as The authors further define.
  • The authors analyze the models to obtain thenew call blocking probabilityfor each call class (i.e., slow or fast); i.e., the probability that a new call of that class is blocked on arrival to the system.

A. The Approximate Analysis Approach

  • The authors define the following stochastic processes for .
  • Hence, the authors have a finite state space for this process.
  • In principle, the stationary blocking and dropping probabilities can be obtained from this stationary distribution.
  • The authors resort to an approximate analysis technique similar to the one adopted by several previous researchers in this area (for example, [8] and [16]).
  • The process in the cell, i.e., , is analyzed in isolation, assuming that the arrival process of handoffs from the neighboring cells is Poisson.

B. Additional Notation for the Analysis of an Isolated Cell in the Homogeneous Model

  • For the homogeneous model, in the stationary regime, the authors drop the superscript from the various notations.
  • Define arrival rate of new fast calls in a macrocell; these are serviced in the macrolayer (thus, ); arrival rate of handed-off fast calls in the macrolayer; arrival rate of fast calls in the macrolayer due to mobility change of slow calls in the microlayer; and total arrival rate of fast calls in the macrolayer.
  • The dependence of these rates on the various random variables defined in Section III-A is shown in Section III-B1.
  • A handed-off call can enter any one of itsneighbors with equal probability.
  • These arrivals occur from all theneighbors of a cell.

C. Analysis of the Isolated Cell Model Without Repacking

  • The isolated cell model comprises groups of servers each, corresponding to the microcells, and one group of servers corresponding to the macrolayer channels.
  • The authors approximate this dependence by using the stationary probabilities obtained for and hence model as a Markov chain with state space .
  • A fast call becomes a slow call and is retained in the macrolayer if all the channels in its corresponding microcell in the microlayer are occupied.
  • There are two nodes, 1 and 2; node 1 represents the arrival process and node 2 the service process.
  • With these new rates, the next iteration is performed.

A. System Parameters for the Numerical Results

  • The number of channels allocated to each cell is 80; with a reuse factor of three between the cells, this would mean that there are 240 channels available in the system.
  • A reuse factor of four is assumed in the microlayer; hence, the set of channels allocated to the microlayer is partitioned into four sets.
  • When a macrocell is divided into microcells, the area of the microcell is times the area of the macrocell.
  • Assuming that fast mobiles are five times as fast as the slow mobiles, the sojourn rates of the fast and slow calls (in macrocells and microcells, respectively) are related by .
  • Note that repacking of slow calls will always help to reduce the blocking probability of fast calls, but may increase or decrease the blocking probability of slow calls.

C. Analysis and Simulation Results for the Multicell Model

  • A multiple macrocell system is analyzed using their iterative a alysis and using a multicell simulation; graphs between the Erlang load and the blocking probability are plotted for the parameter values , and .
  • Figs. 6–9 show the results without slow call repacking.
  • K. Maheshwari, “Performance analysis of microcellization for supporting two mobility classes in cellular wireless networks,” Master’s thesis, Indian Instit.
  • Since 1988, he has been with the Department of Electrical Communication Engineering, Indian Institute of Science, Bangalore, where he is now a Professor.

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 49, NO. 2, MARCH 2000 321
Performance Analysis of Microcellization for
Supporting Two Mobility Classes in Cellular
Wireless Networks
Krishnan Maheshwari and Anurag Kumar
Abstract—We study the call blocking performance obtained by
microcellizing a macrocell network. Each macrocell is partitioned
into microcells, and some of the channelsoriginally allocatedto the
macrocell are assigned to the microlayer cells according to a reuse
pattern. The arriving calls are classified as fast or slow; fast calls
are always assigned only to macrocell channels, whereas for slow
calls a microcell channel is first sought. Slow calls may be allowed
to overflow to the macrolayer, but may be repacked to vacated mi-
crocell channels. Calls can change their mobility class during a con-
versation. We develop an approximate analysis for computing the
slow and fast call blocking probabilities in such a system. We adopt
the technique of analyzing an isolated macrocell with the Poisson
arrival assumption and then iterating on the stationary analysis
of the isolated macrocell to obtain stationary results for the mul-
ticell system. Simple, but accurate approximations are developed
for analyzing the isolated macrocell and its associated microcells.
The analyses based on the approximate isolated cell model are val-
idated against simulations of a multicell model.
Index Terms—Fast and slow mobiles, macrocells, microcells,
repacking, TDM cellular wireless networks, traffic engineering of
TDM cellular networks.
I. INTRODUCTION
I
N CELLULAR wireless mobile telephony systems, a de-
crease in the size of the cells allows more frequency reuse
in a given area. With the decrease in size of the cells, however,
there is an increase in the number of cell boundaries that a mo-
bile unit crosses. These boundary crossings stimulate handoffs
and location tracking operations. Thus, the signaling capacity
of the signaling processors (in the base stations and the mobile
switching centers) can limit the call handling capacity of a cel-
lular system as the cell size is decreased. These issues are dis-
cussed in [7].
One way of controling the increase of signaling traffic, while
deriving the frequency reuse advantage of smaller cells, is to
consider a cellular (macrocellular) network and subdivide the
large cells into smaller microcells (see [14]). Radio channels are
allocated to macrocells and to microcells. Each mobile call is
then classified as belonging to one of two mobility classes, fast
Manuscript received August 18, 1997; revised January 4, 1999. A part of the
work of A. Kumar was done during his sabbatical at the Wireless Information
Network Lab (WINLAB) Rutgers University, Piscataway, NJ.
K. Maheshwari is with Bell Laboratories, Lucent Technologies, Holmdel, NJ
07733 USA (e-mail: mahe@lucent.com).
A. Kumar is with the Department of Electrical Communication En-
gineering, Indian Institute of Science, Bangalore 560012, India (e-mail:
anurag@ece.iisc.ernet.in).
Publisher Item Identifier S 0018-9545(00)02556-1.
and slow. A call that originates at or terminates on a slow mobile
(henceforth referred to as a slow call) is allocated to a channel in
the microcell in which the mobile is currently located, whereas a
fast call is allocated to a macrocell. It can be expected that, with
appropriate engineering of such a system, more traffic can be
handled, with a given number of channels and a required grade
of service, while limiting the increase of signaling traffic on the
network. See [1], [3], [9], and [22] for further discussions of
such multitier cellular network architectures.
The main contribution of this paper is to develop an approx-
imate analysis for calculating the probabilities of call blocking
in a model of a microcellular network; the analysis is verified
by simulations of the multicell model. The scenario that we are
concerned with is that there is a macrocellular network, with a
given frequency allocation to each cell. Each macrocell is then
microcellized, and the original frequencies assigned to each cell
are partitioned between the microcells and the original macro-
cell.
1
A call that is handled by a channel in a macrocell is said
to be in the macrolayer while a call that is handled by a channel
in a microcell is said to be in the microlayer.
For the purpose of this study, we assume that a speed
threshold, used for classifying the mobiles, has been deter-
mined. A call is identified as fast or slow by the cellular
system. Approaches for carrying out such classification are
proposed in [10], [13], and [22]; we assume, as in [9], that such
classification has already been done on call arrival. A fast call
is allocated to a macrolayer channel in the macrocell that it is
located, and a call that is identified as slow is allocated to a
microlayer channel in the microcell that it is located. A call is
blocked in a layer if all the channels in that layer are occupied.
A slow call that is blocked in the microlayer is attempted to be
assigned a channel in the macrolayer. These calls are said to
overflow from the microlayer to the macrolayer. A slow call is
thus blocked in the system only if channels in both the macro-
cell and the microcell (in which it is located) are occupied.
A fast call is blocked if all the channels in the macrocell to
which it belongs are occupied. Overflow of slow calls to the
macrolayer may give them undue advantage over the fast calls;
to reduce this advantage, one possibility is that if there are slow
calls in the macrolayer from a particular microcell, one of these
calls is moved to the microlayer whenever a call departs from
that microcell. We call this procedure repacking.
1
Clearly, there are other, more efficient, channel allocation schemes, and our
analysis approach applies to any static allocation scheme. The particular alloca-
tion that we have described here is perhaps the first that a cellular operator may
adopt, as it does not disturb an already established frequency plan.
0018–9545/00$10.00 © 2000 IEEE

322 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 49, NO. 2, MARCH 2000
In reality, mobiles do not movewith constant speeds. A speed
change occurs when a mobile moves from a more crowded area
to a less crowded area or if a mobile encounters a traffic signal.
This aspect is also included in our model by allowing calls to
undergo mobility change; i.e., a fast call can become a slow call
and vice versa.
We make the standard stochastic assumptions; i.e., Poisson
new call arrivals, exponential channel holding times, and
exponential cell sojourn times. While the entire multicellular
system can be characterized by a Markov process with many
dimensions and a complex state space, obtaining performance
measures directly from this characterization is an intractable
problem. Our approximate analysis approach is an extension of
the iterative technique that has been used in the past for macro-
cellular networks (see, for example, [5], [8], [9], and [16]).
Each cell is analyzed in isolation, assuming Poisson processes
for handoff arrivals into the cell. Blocking probabilities from
this analysis yield handoff arrival rates for the next iteration.
These iterations are continued until an appropriate convergence
criterion is met. The main effort in adapting this standard
approach to our problem is the isolated macrocell analysis,
especially when overflows, repacking, and mobility changes
are introduced. We develop approximations for these analyses
and show that the numerical results obtained compare favorably
with those obtained from a detailed simulation. Whereas the
analysis is based on iterative calculations on an isolated cell, the
simulation is of a multimacrocell system and actually simulates
call handovers between cells, slow call overflow and repacking
between macrocells and microcells, and mobility changes.
Related work on this problem has appeared in [4], [5], [9],
[10], [13], [21], and [22]. In [21], a cellular system model with
call overflow and repacking between two layers of overlapping
cells is considered. There are no call mobility considerations in
this paper. The technique is based on the observation that, with
repacking, the underlying Markov chain is equivalent to that of
a certain circuit switched network. The Erlang fixed point ap-
proach is used to approximately analyze this network. The ap-
proach, however, leads to a number of “link” constraints that is
exponential in the number of cells. The accuracy of the results
is found to vary from 15% to 40% depending on the number of
channels. In [9], a hierarchical model with three layers is consid-
ered; there are two call classes, and calls can overflow to higher
layers. Overflow processes are modeled as interrupted Poisson
processes (IPP’s) and are not repacked. Mobility changes are not
considered, and no simulation results are provided. In [4], three
types of calls are considered in a single cell with a two-tier ar-
chitecture. The types of calls are classified on the basis of their
access to the different tiers. The model does not include han-
dovers or repacking. In [5] and [10], a nonhomogenous system
(cell sizes are different, arrival rates vary from cell to cell, ar-
bitrary routing between cells, and a general overlap structure
between layers) is analyzed by iterating all the cells together.
In [5], the overflow processes between layers are modeled by
using two moments, whereas in [10] the composite overflow
processes are approximated as Poisson. In [10], calls are iden-
tified as being fast or slow depending on their sojourn time in
a cell; a call identified as fast is handed over to a higher layer
macrocell. These papers do not consider repacking, and only an-
alytical approximations are presented without validating simu-
lation results.
In [22], a procedure for identifying the mobility class of a call
(i.e., fast call or slow call) is proposed. A mobile determines
its mobility based on its microcell sojourn time. This informa-
tion is used to determine the base station (at the macrocell or at
the microcell) which will handle the call during origination or
handoff of the call. A similar approach for identifying fast calls
is proposed in [13], and in addition analysis of grade-of-service
is done for a two-layer system. The latter paper, however, does
not consider slow call repacking and mobility changes. Also,
only analytical results are presented.
The remainder of the paper is organized as follows. In Sec-
tion II, we describe the model, list the notation used, and de-
finetheperformance measures. An approximate analysis for this
model is developed in Section III. In Section IV, we provide nu-
merical results that show how accurate the analysis is in com-
parison with simulations of the model. The conclusions and an
outline of further work are presented in Section V.
II. T
HE MODEL,NOTATION, AND TERMINOLOGY
A. Handovers, Repacking, and Signaling
We define a handoff (or handover) as any event that causes
the system to seek a new channel for an existing call in the
system. Handoffs occur due to cell boundary crossings (i.e.,
a“radio–reason handoff), mobility changes, or repacking. A
radio–reason handoff occurs whenever a slow call crosses a mi-
crocell boundary, or a fast call crosses a macrocell boundary.
When a fast call changes mobility to become a slow call, an
attempt is made to assign it to a channel in the microcell in which
it is located. If this attempt fails, then the call is retained in the
macrolayer. When a slow call in the microlayer changes mo-
bility, an attempt is made to assign it to a channel in the macro-
layer. If this attempt fails, the call is not retained in the micro-
layer, but is dropped. If this call is retained in the microlayer, it
will encounter a large number of cell boundary crossings. This
is not desirable since, after adding substantially to the signaling
traffic, it is very likely to get dropped anyway. No harm is done
by dropping the call provided the overall call dropping prob-
ability is better than the operator's promised grade-of-service
(say, e.g., 0.1%). Channel reservation for fast calls in the macro-
layer can be used to control this dropping probability. We have
not considered channel reservation in this paper, but see [19].
If a slow call in the macrolayer moves across a microcell
boundary, then an attempt is always made to hand the call over
to a microcell channel. If there is no such channel, then the slow
call is retained in the macrolayer.
Handovers are also caused by the repacking of slow calls oc-
cupying macrolayer channels; i.e., slow calls that are assigned
channels in the macrolayer are moved back to the microlayer
on availability of channels in their respective microcells. Chan-
nels in the macrolayer are thus freed up. Note that the repacking
of a slow call in this way is triggered by a slow call depar-
ture from a microcell; a slow call in the macrolayer does not
need to constantly monitor the occupancy of its microcell. Thus,
slow calls are handled in a macrocell only when their corre-
sponding microcell isfully occupied.This increases the capacity

MAHESHWARI AND KUMAR: PERFORMANCE ANALYSIS OF MICROCELLIZATION 323
of the system, butadditional signaling will be incurred due to the
channel reassignments.
Channel reassignments and handoffs cause signaling traffic,
and, hence, load the call processing systems. The set of events
that contribute to the signaling traffic are new call arrivals, cell
boundary crossings, mobility changes, and repacking.
B. Model Parameters and Notation
New call arrival processes for the various macrocells are in-
dependent Poisson processes. Each arrival into a macrocell is
fast or slow with a certain probability. The probability that an
arriving call is fast or slow may be different in different macro-
cells. A call arriving to a macrocell is assumed to be located in
a particular microcell within the macrocell with a certain prob-
ability. The conversation time for a call and a mobile's sojourn
time in a cell are assumed to be exponentially distributed. Fur-
thermore, the intervals at which a mobile changes its mobility
are also assumed to be exponentially distributed. In practice,
these intervals will include the time to reliably detect the mo-
bility change.
Macrocells are numbered and are indexed by integers
. There are microcells in the th macrocell. The
microcells in the
th macrocell are numbered using double
indexes
. Define:
number of channels assigned to macrocell in the
macrolayer;
number of channels assigned to microcell in macro-
cell
;
total arrival rate of new calls (fast and slow) in macro-
cell
;
probability that a new call in macrocell is a fast call;
probability that a call originating in macrocell is
physically located in microcell
;
mean conversation time of a call in the system; taken
to be one always; thus, all times are normalized to the
mean call duration;
mean sojourn time of a slow call in the microcell ;
mean sojourn time of a fast call in the macrocell ;
rate of change of mobility of fast calls;
rate of change of mobility of slow calls.
The mobility change model is to be understood as follows: a call
that is now a slow call will become a fast call after a random time
that is exponentially distributed with mean
, provided, of
course, that the conversation lasts that long. We further define:
probability that a call leaving macrocell enters
macrocell
;
probability that a call leaving microcell enters
microcell
.
Performance Measures: In this paper, we analyze the
models to obtain the new call blocking probability for each call
class (i.e., slow or fast); i.e., the probability that a new call of
that class is blocked on arrival to the system. We denote the
blocking probabilities by
and . Other performance
measures of interest would be: handoff blocking probabilities,
call dropping probabilities, and the system signaling rate for
setting up new calls and handling handoffs.
III. A
NALYSIS OF THE MODEL
A. The Approximate Analysis Approach
There are
cells, indexed by , and cell
has microcells, indexed by . We define
the following stochastic processes for
.
For
, define:
number of fast calls in the macrolayer of cell ;
number of slow calls in the macrolayer of cell
and for
number of slow calls in the macrolayer of cell that
are located (at time
)inmicrocell ; [of course,
];
number of slow calls in the microlayer that are lo-
cated (at time
)inmicrocell
and denote by
With our stochastic assumptions (Poisson new call arrivals,
exponentially distributed channel holding times, exponentially
distributed cell sojourn times, and Markovian call routing be-
tween cells), the stochastic process
is a Markov process. The number of calls in each layer is re-
stricted by the total number of available channels in that layer.
Hence,we have a finitestate space for this process. For finiteand
positive values of all the rate parameters, this Markov process is
irreducible and hence positive recurrent; thus, a stationary distri-
bution exists. In principle, the stationary blocking and dropping
probabilities can be obtained from this stationary distribution.
Owing to the several special features of this model (handoffs,
overflows, repacking, and mobility change), the stationary dis-
tribution does not havea “product form.” Furthermore, owing to
the large size of the state space, direct numerical computation
is intractable. Consequently, we resort to an approximate anal-
ysis technique similar to the one adopted by several previous
researchers in this area (for example, [8] and [16]).
The process in the cell
, i.e., , is analyzed in iso-
lation, assuming that the arrival process of handoffs from the
neighboring cells is Poisson. This is done for every cell, and,
using the intercell routing probabilities, handoff rates between
the various cells are obtained. The isolated cell analyses are re-
peated with these new handoff rates. This iterative process is
begun with some initial value of handoff rates entering each
cell (e.g., zero rates). If this iterative calculation converges (as
it does in all the cases that we have studied), then the limiting
probability distribution provided by the iteration at the
th cell
is taken to be the stationary distribution of the
th marginal of
the process
. Since new call arrivals are
Poisson, this yields an approximation for the new call blocking
probability.
In this paper, we: 1) develop the isolated cell analysis
with Poisson arrivals, with macrocells, microcells, repacking
and mobility changes and 2) examine the accuracy of this
approximate analysis procedure for a homogeneous cellular
network (i.e., all cells are identical, having the same number

324 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 49, NO. 2, MARCH 2000
of microcells, arrival rate, mean call holding time, and sojourn
time, and also the same number of channels in the macrolayer
and microlayer). Such a homogenous model can be used to
model the central cells in a large array of cells in which the
nonhomogeneity is only in the boundary cells. Note that the
models analyzed in [9] and [13] are also homogenous.
B. Additional Notation for the Analysis of an Isolated Cell
in the Homogeneous Model
For the homogeneous model, in the stationary regime, we
drop the superscript
from the various notations. We denote
the stationary marginal random variable for
by ,
for
by , for by , and that for
by . Also, for the homogeneous case, the notation in Sec-
tion II-B yields
.
Define
arrival rate of new fast calls in a macrocell; these
are serviced in the macrolayer (thus,
); arrival
rate of handed-off fast calls in the macrolayer;
arrival
rate of fast calls in the macrolayer due to mobility change of
slow calls in the microlayer; and
total arrival rate of fast
calls in the macrolayer. Hence
(1)
We also define the following arrival rates of slow calls.
arrival rate of new slowcalls in a microcell [hence,
]; arrival rate of slow handoff calls in a microcell;
arrival rate of slow calls in a microcell due to change of
mobility of fast calls in the macrolayer;
the total arrival
rate of slow calls in a microcell. Hence
(2)
Furthermore, we denote by
the rate of arrival of overflow
slow calls to a macrocell. The rates
and are
a priori unknown and are calculated iteratively after assuming
an initial value for them. The dependence of these rates on the
various random variables defined in Section III-A is shown in
Section III-B1.
1) Calculation of Various Stationary Rates: The rate at
which fast calls handoff from a macrocell is
. A handed-off
call can enter any one of its
neighbors with equal probability.
All the cells are assumed to be identical and, hence,
(see the stationary marginal random variables defined above)
is taken as the expected number of fast calls in any cell in the
macrolayer. It is clear that in the stationary regime, the arrival
rate due to handoffs from a single neighbor cell is
.
These arrivals occur from all the
neighbors of a cell. Hence
(3)
is the expected number of slow calls in the macrolayer,
and
is the expected number of slow calls in a microcell.
Assuming homogeneity among the microcells within a cell also,
we have
. Since slow calls oc-
cupying macrolayer channels are always attempted to be handed
off to the microlayer when they cross a microcell boundary, we
have
(4)
Also, slow calls from any of the
microcells of a macrocell
may become fast calls at rate
. Therefore
(5)
Since all the microcells in a cell are considered to be identical,
a fast call in the macrocell is located in any one of the micro-
cells with probability
. is the rate at which fast calls
in the macrolayer generate slow calls due to mobility change.
Hence
(6)
and are again functions of the net arrival
and net service rates of fast and slow calls in a cell. Hence,
these can be computed iteratively and then used to compute the
blocking probabilities.
C. Analysis of the Isolated Cell Model Without Repacking
In this model, a slow call that arrives in a cell and is served
in the macrolayer, owing to the nonavailability of a channel in
the microlayer, is retained in the macrolayer until it requires
radio–reason handoff, or crosses a microcell boundary, or until
it completes the conversation. If the slowcall crosses a microcell
boundary (even if it is in the same macrocell), then a channel is
first sought for it in the microcell that it enters.
The isolated cell model comprises
groups of servers
each, corresponding to the microcells, and one group of
servers corresponding to the macrolayer channels. Slow calls
arrive to the microcell
in a Poisson process
at the rate
; fast calls arrive to the macrolayer channels in a
Poisson process at the rate
. A slow call finding its microcell
full overflows to the macrocell channels. A fast call holds a
macrocell channel for an exponentially distributed duration
with rate
, but changes class to slow at the rate .
Similarly, a slow call in the macrolayer holds a channel for
an exponentially disributed time with rate
, but changes
mobility at the rate
. Observe that, without mobility changes,
this model is just the classical overflow model that arises in
telephone trunk engineering. Owing to the large number of
microcells, we assume that the overflow process is Poisson.
We will show how this approximation works in comparison
with simulations. In contrast in [9] the overflow process is
modeled by an IPP; for our situation, where we are modeling
several new features, considering the additional state of the IPP
would further complicate the analysis. Simulations show that
our approximations are adequate.
1) Stationary Analysis of the Microlayer: For a microcell
in isolation, assuming Poisson arrival processes,
is a
Markov chain on
, with the transition rate diagram
shown in Fig. 1; here
is as defined in Section III-B.

MAHESHWARI AND KUMAR: PERFORMANCE ANALYSIS OF MICROCELLIZATION 325
Fig. 1. Transition rate diagram for the microcell process
Z
(
t
)
, with no repacking.
Hence, the stationary probability, is calculated
from the Erlang formula, Erlang
, which is defined as
Erlang
(7)
where
is the offered load in Erlangs and is given for our model
as
.
Finally,
[as needed in (4) and (5)] is computed, using
Little's theorem, as
(8)
2) Stationary Analysis of the Macrolayer: Slow calls
blocked from microcells, or those changing mobility, arrive
into the macrolayer. Hence, in the isolated cell model, the
process
depends on the process .If
the number of microcells in a macrocell is large, then we can
expect that the dependence of the macrolayer process on any
particular microcell will be small, and also the microcells will
be weakly dependent among themselves. With this in mind, we
approximate this dependence by using the stationary probabili-
ties obtained for
and hence model as a
Markov chain with state space
.
The macrolayer has new fast call arrivals in a Poisson stream.
A fast call can leave the macrolayer for one of three reasons: on
call completion, or on cell boundary crossing, or on a mobility
change with the probability that the microcell in which it is lo-
cated has a free channel. To account for this last possibility, we
need the conditional probability distribution of
, condi-
tioned on the states of the process
. However, as
stated earlier, as an approximation, we use the stationary prob-
abilities of the process
. Hence, the rate at which a fast
call leaves the macrolayer due to mobility change is calculated
as
. A slow call leaves the macrolayer either
on call completion or on cell boundary crossing; from the point
of view of a single isolated cell model, a slow call, in the macro-
layer, that crosses its microcell boundary is seen as leaving the
macrolayer (since an attempt is made to serve it in the micro-
layer of the neighboring cell; see Section II); actually, if the
neighboring microcell is full, then the call may be retained in
the macrolayer, but this will be viewed as a new overflow arrival
from the microlayer in our analysis. Let
denote the total rate
at which a fast call leaves a macrocell in the macrolayer and
denote the total rate at which a slow call leaves the macrolayer.
From the arguments above, we have the relations
(9)
(10)
Slow calls arrive into the macrolayer when the microcell
in which they are located has no free channels. New and
Fig. 2. Transition rate diagram for macrocell process
f
(
X
(
t
)
;Y
(
t
))
g
, with
no repacking.
handed-off slow calls arrive to each microcell at the rate
. Hence, the rate of arrival of overflow slow calls to
the macrolayer is
(11)
The arrival rate of fast calls to the macrolayer
is given by (1)
and the expressions in Section III-B1.
A fast call becomes a slow call and is retained in the macro-
layer if all the channels in its corresponding microcell in the mi-
crolayer are occupied. As above, we assume that a fast call that
becomes slow finds its corresponding microcell full with prob-
ability
. Furthermore, a slow call in the macrolayer
retains its channel if it becomes fast. With these observations we
define the rates
(12)
(13)
It is now clear that, with the assumptions made and the nota-
tion defined,
has the transition diagram shown
in Fig. 2.
It is easily seen that the transition diagram in Fig. 2 is the same
as that of the closed Markovian queueing network shown in
Fig. 3. There are two nodes, 1 and 2; node 1 represents the arrival
process and node 2 the service process. There are three types
of calls: the incoming calls that are only at node 1, and fast and
slowcallsthat are at node 2. The service rate at node 1 is
;
customers at node 1 depart as fast or slow calls according to
the probabilities
and where

Citations
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Journal ArticleDOI
TL;DR: It is observed that the overall resource utilization can be maximized when the admission regions for voice and data services in a cell and a WLAN are properly configured.
Abstract: In the interworking between a cellular network and wireless local area networks (WLANs), a two-tier overlaying structure exists in the WLAN-covered areas. Due to the heterogeneous underlying quality-of-service (QoS) support, the admission of traffic in these areas has a significant impact on QoS satisfaction and overall resource utilization, especially when multiple services are considered. In this paper, we analyze the performance of a simple admission strategy, referred to as WLAN-first scheme, in which incoming voice and data service requests always first try to get admission to the WLAN whenever it is available. It is observed that the overall resource utilization can be maximized when the admission regions for voice and data services in a cell and a WLAN are properly configured

124 citations


Cites background from "Performance analysis of microcelliz..."

  • ...A service request rejected by its first-choice network can just leave the system or further try to access the other network [1]....

    [...]

  • ...Third, in cellular/WLAN interworking, it is not practical to allocate resources based on fast/slow user mobility differentiation [1,2] as in hierarchical cellular networks....

    [...]

Journal ArticleDOI
TL;DR: It is concluded that an improvement in energy consumption in cellular wireless networks by two orders of magnitude, or even more, is possible.
Abstract: Conventional cellular wireless networks were designed with the purpose of providing high throughput for the user and high capacity for the service provider, without any provisions of energy efficiency. As a result, these networks have an enormous Carbon footprint. In this paper, we describe the sources of the inefficiencies in such networks. First, we present results of the studies on how much Carbon footprint such networks generate. We also discuss how much more mobile traffic is expected to increase so that this Carbon footprint will even increase tremendously more. We then discuss specific sources of inefficiency and potential sources of improvement at the physical layer, as well as at higher layers of the communication protocol hierarchy. In particular, considering that most of the energy inefficiency in cellular wireless networks is at the base stations, we discuss multi-tier networks and point to the potential of exploiting mobility patterns in order to use base station energy judiciously. We then investigate potential methods to reduce this inefficiency and quantify their individual contributions. By a consideration of the combination of all potential gains, we conclude that an improvement in energy consumption in cellular wireless networks by two orders of magnitude, or even more, is possible.

69 citations


Cites background from "Performance analysis of microcelliz..."

  • ...ll. On the other hand, the concept of a microcell underlay to serve users with low mobility and the use of macrocells for users with high mobility were introduced and studied earlier, see e.g., [142]–[144]. The presence of multiple tiers of networks such as a microcell underlay of macrocells is known as Hierarchical Cell Structure (HCS). Unlike femtocells, which are dumb devices as far as coordination ...

    [...]

Journal ArticleDOI
TL;DR: In this paper, the authors present results of the studies on how much Carbon footprint such networks generate and how much more mobile traffic is expected to increase so that this Carbon footprint will even increase tremendously more.
Abstract: Conventional cellular wireless networks were designed with the purpose of providing high throughput for the user and high capacity for the service provider, without any provisions of energy efficiency. As a result, these networks have an enormous Carbon footprint. In this paper, we describe the sources of the inefficiencies in such networks. First we present results of the studies on how much Carbon footprint such networks generate. We also discuss how much more mobile traffic is expected to increase so that this Carbon footprint will even increase tremendously more. We then discuss specific sources of inefficiency and potential sources of improvement at the physical layer as well as at higher layers of the communication protocol hierarchy. In particular, considering that most of the energy inefficiency in cellular wireless networks is at the base stations, we discuss multi-tier networks and point to the potential of exploiting mobility patterns in order to use base station energy judiciously. We then investigate potential methods to reduce this inefficiency and quantify their individual contributions. By a consideration of the combination of all potential gains, we conclude that an improvement in energy consumption in cellular wireless networks by two orders of magnitude, or even more, is possible.

62 citations

Journal ArticleDOI
TL;DR: A simple two-state MMPP/sup (1,2,...,K)/, that takes into account not only the dependence among overflowed calls of the same class but also the correlation among overflowing calls of different classes, is used to approximate overflowed traffic to reduce computational complexity and improve accuracy.
Abstract: A cellular hierarchical network with heterogeneous traffic is considered, where calls with shorter (longer) average call-holding time are assigned to the associated lower (upper) layer. The main contribution of this paper is that an efficient and reasonably accurate analytical method is proposed to calculate performance measures of interest, i.e., new call-blocking probability and forced termination probability for conversational services, new call-blocking probability, forced termination probability, and the average number of assigned time slots for streaming services. In particular, a simple two-state MMPP/sup (1,2,...,K)/, that takes into account not only the dependence among overflowed calls of the same class but also the correlation among overflowed calls of different classes, is used to approximate overflowed traffic to reduce computational complexity and improve accuracy. The methods with the multiclass overflowed traffic being approximated as independent Poisson processes and interrupted Poisson processes are also conducted for comparison. Importantly, it is shown via simulation results that the proposed model generates more accurate results than those obtained with the other two approximation methods. Last but not least, the effect of nonuniform traffic density on performance measures is studied via simulation. It is shown that the nonuniform traffic density may have a significant impact on the performance.

56 citations


Cites methods or result from "Performance analysis of microcelliz..."

  • ..., [13] and [16], provide the simulation results to verify the analytical results....

    [...]

  • ...In particular, the overflowed traffic is approximated as Poisson traffic in [12] and [13], as interrupted Poisson process (IPP) traffic in [14] and [27], and as Markov Modulated Poisson Process (MMPP) traffic in [15], [16], and [23]....

    [...]

Journal ArticleDOI
TL;DR: This paper investigates a bidirectional call-overflow scheme, based on the velocity of the mobile making the calls, and shows that the proposed scheme outperforms others in terms of average hew call blocking and hand off failure probability of the system.
Abstract: With the increase of teletraffic demands in mobile cellular system, hierarchical cellular systems (HCSs) have been adopted extensively for more efficient channel utilization and better GoS (Grade of Services). A practical issue related to HCS is to design a scheme for controlling and allocating call traffic to different layers. There are several strategies to deal with this problem, such as no call-overflow scheme, unidirectional call-overflow scheme and bidirectional call-overflow scheme. The objective of this paper is to investigate a bidirectional call-overflow scheme, based on the velocity of the mobile making the calls. To ensure that hand off calls are given higher priorities, it is assumed that guard channels are assigned in both macrocells and microcells. In order to evaluate the performance of the new scheme and compare the performance of several related schemes, two now models based on a one-dimensional Markov process are developed and analytical results are derived. Theoretical analysis and numerical evaluation show that the proposed scheme outperforms others in terms of average hew call blocking and hand off failure probability of the system. In addition, when the teletraffic to the HCS reaches a certain grade, the GoS is insensitive to the maximum velocity and the velocity threshold which is used to assign calls to different layers in our scheme.

33 citations


Cites background from "Performance analysis of microcelliz..."

  • ...For a slow mobile, its dwell times in microcell and macrocell, tsm and tsM , are different random variables and have the negative exponential distribution with the mean 1= sm and 1= sM , respectively....

    [...]

  • ...1045-9219/03/$17.00 ß 2003 IEEE Published by the IEEE Computer Society free channel, even though its overlaid microcell has many free channels, the fast calls will terminate....

    [...]

References
More filters
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01 Jan 1979
TL;DR: This classic in stochastic network modelling broke new ground when it was published in 1979, and it remains a superb introduction to reversibility and its applications thanks to the author's clear and easy-to-read style.
Abstract: This classic in stochastic network modelling broke new ground when it was published in 1979, and it remains a superb introduction to reversibility and its applications. The book concerns behaviour in equilibrium of vector stochastic processes or stochastic networks. When a stochastic network is reversible its analysis is greatly simplified, and the first chapter is devoted to a discussion of the concept of reversibility. The rest of the book focuses on the various applications of reversibility and the extent to which the assumption of reversibility can be relaxed without destroying the associated tractability. Now back in print for a new generation, this book makes enjoyable reading for anyone interested in stochastic processes thanks to the author's clear and easy-to-read style. Elementary probability is the only prerequisite and exercises are interspersed throughout.

2,480 citations


"Performance analysis of microcelliz..." refers background in this paper

  • ...Hence, the stationary distribution has the following product form (see [12])....

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Journal ArticleDOI
TL;DR: A traffic model and analysis for cellular mobile radio telephone systems with handoff, which shows, for example, blocking probability, forced termination probability, and fraction of new calls not completed, as functions of pertinent system parameters.
Abstract: A traffic model and analysis for cellular mobile radio telephone systems with handoff are described. Three schemes for call traffic handling are considered. One is nonprioritized and two are priority oriented. Fixed channel assignment is considered. In the nonprioritized scheme the base stations make no distinction between new call attempts and handoff attempts. Attempts which find all channels occupied are cleared. In the first priority scheme considered, a fixed number of channels in each cell are reserved exclusively for handoff calls. The second priority scheme employs a similar channel assignment strategy, but, additionally, the queueing of handoff attempts is allowed. Appropriate analytical models and criteria are developed and used to derive performance characteristics. These show, for example, blocking probability, forced termination probability, and fraction of new calls not completed, as functions of pertinent system parameters. General formulas are given and specific numerical results for nominal system parameters are presented.

1,654 citations


"Performance analysis of microcelliz..." refers methods in this paper

  • ...Consequently, we resort to an approximate analysis technique similar to the one adopted by several previous researchers in this area (for example, [ 8 ] and [16])....

    [...]

  • ...Our approximate analysis approach is an extension of the iterative technique that has been used in the past for macrocellular networks (see, for example, [5], [ 8 ], [9], and [16])....

    [...]

Journal ArticleDOI
J. Kaufman1
TL;DR: It is shown that, for the important and commonly implemented policy of complete sharing, a simple one-dimensional recursion can be developed which eliminates all difficulty in computing quantities of interest-regardless of both the size and dimensionality of the underlying model.
Abstract: In recent years, considerable effort has focused on evaluating the blocking experienced by "customers" in contending for a commonly shared "resource." The customers and resource in question have typically been messages and storage space in message storage applications or data streams and bandwidth in data multiplexing applications. The model employed in these studies, a multidimensional generalization of the classical Erlang loss model, has been limited to exponentially distributed storage (or data transmission) times, questions concerning efficient computational schemes have largely been ignored, and the class of resource sharing policies considered has been unnecessarily restricted. The contribution of this paper is threefold. We first show that the state distribution (obtained by previous authors) is valid for the large class of residency time distributions which have rational Laplace transforms. Second, we show that, for the important and commonly implemented policy of complete sharing, a simple one-dimensional recursion can be developed which eliminates all difficulty in computing quantities of interest-regardless of both the size and dimensionality of the underlying model. Third, we show that the state distribution holds for completely arbitrary resource sharing policies.

1,029 citations


"Performance analysis of microcelliz..." refers background in this paper

  • ...It is clear that the process has a product form stationary distribution since we have a multiclass resource sharing model with a coordinate convex partial sharingpolicy (see [11])....

    [...]

Proceedings Article
01 Jan 1986
TL;DR: A traffic model and analysis for cellular mobile radio telephone systems with handoff, which shows, for example, blocking probability, forced termination probability, and fraction of new calls not completed, as functions of pertinent system parameters.
Abstract: A traffic model and analysis for cellular mobile radio telephone systems with handoff are described. Three schemes for call traffic handling are considered. One is nonprioritized and two are priority oriented. Fixed channel assignment is considered. In the nonprioritized scheme the base stations make no distinction between new call attempts and handoff attempts. Attempts which find all channels occupied are cleared. In the first priority scheme considered, a fixed number of channels in each cell are reserved exclusively for handoff calls. The second priority scheme employs a similar channel assignment strategy, but, additionally, the queueing of handoff attempts is allowed. Appropriate analytical models and criteria are developed and used to derive performance characteristics. These show, for example, blocking probability, forced termination probability, and fraction of new calls not completed, as functions of pertinent system parameters. General formulas are given and specific numerical results for nominal system parameters are presented.

920 citations


"Performance analysis of microcelliz..." refers methods in this paper

  • ...Our approximate analysis approach is an extension of the iterative technique that has been used in the past for macrocellular networks (see, for example, [5], [8], [9], and [16])....

    [...]

  • ...Consequently, we resort to an approximate analysis technique similar to the one adopted by several previous researchers in this area (for example, [8] and [16])....

    [...]

Journal ArticleDOI
TL;DR: A taxonomy of channel assignment strategies is provided and the complexity in each cellular component is discussed, and the required intelligence distribution among the network components is defined.
Abstract: A taxonomy of channel assignment strategies is provided, and the complexity in each cellular component is discussed. Various handover scenarios and the roles of the base station and the mobile switching center are considered. Prioritization schemes are discussed, and the required intelligence distribution among the network components is defined. >

494 citations

Frequently Asked Questions (1)
Q1. What have the authors contributed in "Performance analysis of microcellization for supporting two mobility classes in cellular wireless networks" ?

The authors study the call blocking performance obtained by microcellizing a macrocell network.