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CHAPTER-II BACKGROUND AND REVIEW OF LITERATURE
2.1 Wireless Network Architecture
2.1.1 Mobile Station
2.1.2 Base Station Sub-system
2.1.3 Network and Switching System Components
2.1.4 Operation and Maintenance Sub-system
2.1.5 Interfaces
2.2 Network Availability, Reliability and Survivability
2.3 Telecommunications Traffic
2.3.1 Unit of Traffic
2.3.2 Mathematical Model of Traffic
2.3.3 Lost Call System and Grade of Service
2.4 Modeling and Simulation
2.4.1 Modeling
2.4.2 Simulation
2.4.3 Procedure for Monte-Carlo Simulation
2.4.4 Analytical Versus Simulation Modeling
2.4.5 Discrete Event Simulation
2.5 Concepts of Economic Growth and Productivity
2.5.1 Economic Activity and Concept of Productivity
2.5.2 Cobb-Douglas Production Function
2.5.3 Economic Growth and Productivity
2.5.4 Total Factor Productivity
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Chapter 2
Background and Review of Literature
2.1 Wireless Network Architecture:
Wireless communications networks have spread widely everywhere than
anyone could have imagined when the cellular concept was first
developed in 1960s and 1970s. According to Theodore (2012), the
widespread success of cellular has led to the development of newer
wireless systems and standards for many other types of
telecommunication traffic besides mobile voice telephone calls. There
are several types of wireless technologies such as fixed wireless, mobile
wireless, wireless in local loop, and personal communications systems.
Fixed wireless access is a technology introduced with new standards and
technology in the wireless networks to replace fiber optic or copper lines
between fixed points of several kilometers apart. The cellular network,
second generation or 2G conform to the second-generation cellular
standards. Global System for Mobile Communications (GSM) is a
second-generation cellular system standard and it was the world’s first
cellular system to specify digital modulation and network level
architecture and services. Since the second-generation, 2G sets the
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foundation of the wireless network; this research considers the 2G
architecture. About seventy-five percent of the total BTSs of BSNL
Manipur belong to 2G.
In a cellular system, the geographical area is divided into
adjacent, non-overlapping, hexagonal shaped cells. Each cell is
equipped with transmitter and receiver called base transceiver station
(BTS) to communicate with the mobile units in that cell. Mobile
switching station coordinates the handoff of mobile units crossing cell
boundaries. Cellular systems are based on the concept of frequency
reuse: the same frequency is used by several sites, which are far enough
from one another, resulting in a tremendous gain in system capacity.
The counterpart is the increased complexity, both for the network and
the mobile stations, which must be able to select a station among several
possibilities, and the infrastructure cost because of the number of
different sites. The system hands over calls from transmitter to
transmitter as customers move around in their vehicles. Cell splitting
is a technique introduced in the network and the technique allows more
customers access the system simultaneously by dividing the area served
by each transmitter when there is requirement of more capacity. One of
the most important concepts for any cellular telephone system is that
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of multiple access meaning that multiple simultaneous users can be
supported through frequency reuse. In other words, a large number of
users share a common pool of radio channels and any user can gain
through, as merely a portion of the limited radio spectrum, which is
temporarily allocated for a specific purpose, such as someone’s phone
call.
The GSM system architecture consists of three major
interconnected subsystems. The subsystems interact among themselves
and in addition, with the users through certain network interfaces. The
three subsystems are: 1. Network switching subsystem (NSS) 2. Base
station subsystem (BSS) and 3. Operation support subsystem (OSS).
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Base Station Subsystem
Network Switching Subsystem
A-Interface
Operation Support Subsystem
Air Abis Interface Interface
Figure 2.1: Architecture of GSM network
BTS
BTS
BTS
TCU
BSC
MSC
VLR
HLR
AUC
Operation
& Maintenance
Center
EIR
PSTN
ISDN
Data NW
MS
HLR- Home Location Register VLR- Visitor Location Register EIR- Equipment Identity Register AUC- Authentication Center ISDN- Integrated Services Digital Network
BTS- Base Transceiver Station MSC- Mobile Switching Center MS - Mobile Station TCU- Transcoder Unit PSTN- Public Switched Telephone Network
The network and switching subsystem is responsible for performing call
processing and subscriber related functions. It includes the following
functional units:
- Mobile services Switching Centers (MSC)
- Home Location Register (HLR)
- Visitor Location Register (VLR)
- Authentication Center (AUC)
- Equipment Identity Register (EIR)
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2.1.1 Mobile Station:
An MS is used by a mobile subscriber to communicate with the mobile
network. The range or coverage area of an MS depends on the output
power of the MS. GSM MS consist of 1. A mobile terminal and 2. A
Subscriber Identity Module (SIM). The SIM card contains a unique
International Mobile Subscriber Identity Module (IMSI) used to identify
the subscriber of the system. The SIM contains subscriber related
information on the user’s side of the radio interface. It is basically a
smart card.
2.1.2 Base Station Subsystem:
The BSS also known as the radio subsystem provides and manages radio
transmission paths between the mobile stations and the Mobile
Switching Center. The BSS is in direct contact with the mobile stations
through the radio interface. The BSS is comprised of the following
functional units:
- Base Station Controller (BSC)
- Base Transceiver Station (BTS)
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Mobile Switching Center, Base Station Controller, TCU and PSTN Telephone Exchange
Mobile Switching Center (MSC-Ericsson GSM)
Place: Telephone Bhawan, Imphal
Base Station Controller (Ericson BSC)
Place: Telephone Bhawan , Imphal
Base Station Controller (Nortel BSC)
Place: Telephone Bhawan, Imphal
Transcoder Unit (TCU)
Place: Telephone Bhawan, Imphal
CDMA-MSC
Place: Telephone Bhawan, Imphal
PSTN OCB Trunk Automatic Exchange (TAX)
Place: Telephone Bhawan, Imphal
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The BSS may consist of one or more BSCs, which connect to a single
MSC, and each BSC typically controls many BTSs depending on their
traffic capacity. The BTSs may be co-located with the BSC or may be
placed in remote locations. The BTSs are connected to BSC physically
through microwave link or dedicated optical fiber line. BSC has
frequency administration tasks. The other tasks include control of a
BTS, and exchange functions. It handles radio- channels setup,
frequency hopping, and handovers. The BSC is the in charge of all radio
interface management through the remote command of the BTS and the
mobile station, mainly the allocation and release of radio channels and
the handover management. Several BTSs are connected to BSC on one
side and other side of the BSC is connected to the MSC. BSC has
substantial computational capability and it functions like a typical small
switch. More than 190 BTSs of BSNL Manipur are connected to two
BSCs located at Imphal.
Base Station or Base Transceiver Station:
The BTS controls the radio interface to the Mobile Station within a
cellular network. The BTS comprises the radio equipment such as
transceivers and antennas which are needed to serve each cell in the
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network. A BTS is usually located in the center of a cell. Physical
location of the radio equipment is referred by a cell site and the radio
equipment provides coverage within a cell. BTSs are placed in the field
to transfer a call to a customer’s handset i.e. Mobile Station (MS), and
there are between one and sixteen transceiver, each of which represents
a separate RF channel. Normally, a typical BTS may cover an area of 30
to 40 square kilometers though the maximum distance an MS can be
from a BTS is 35 kilometers. However, in a congested urban location
where traffic is high, the BTS coverage area is much smaller. BTS can
be considered as complex radio modems and have little other function.
2.1.3 Network and switching subsystem components:
Mobile services Switching Center (MSC):
The NSS handles the switching of GSM calls between external networks
and the BSCs in the radio subsystem and is responsible for managing
and providing external access to several customer databases. The MSC
is the central unit in the NSS and controls the traffic among all the
BSCs. The MSC is the interface of the cellular network to the PSTN
(Public Switched Telephone Network), Integrated Services Digital
Network (ISDN), public data networks, private data networks and other
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mobile networks. MSC performs the telephony switching functions for
the mobile network. The primary functions of an MSC include-
switching and call routing, charging of mobile calls, service
provisioning, communication with HLR, communication with VLR,
communication with other MSCs and control of connected BSCs. MSC
has functionality to handle a mobile subscriber, such as registration,
authentication, location updating, handovers, and call routing to a
roaming subscriber. The MSC also provides the network with the
specific data about individual mobile stations. The MSC interfaces with
BSS on one other side and with the external networks on the other.
Gateway functionality enables an MSC to interrogate a network’s HLR
in order to route a call to a Mobile Station (MS). Such an MSC is called
a Gateway MSC (GMSC). Any MSC in the mobile network can
function as a gateway by integration of the appropriate software.
Home Location Register (HLR):
The HLR is centralized database of the network. It stores and manages
all mobile subscription belonging to a specific operator. It acts as a
permanent store for a person’s subscription information until that
subscription is cancelled. The information stored in the HLR includes:
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- Subscriber identity e.g. IMSI (International Mobile Subscriber
Number)
- Subscriber supplementary services
- Subscriber location information
- Subscriber authentication information
In addition to the above information, the HLR stores some temporary
data pertaining to visitors. It has address of the current visitor location
register (VLR) in which mobile stations are currently administered, the
mobile numbers to which calls are to be forwarded and transient
parameters for authentication and ciphering. The SIM card stores the
IMSI, which has information to identify a subscriber within GSM
system. The first three digits of the IMSI identify the Mobile Country
Code (MCC) and the next two digits are the mobile network code
(MNC). Up to ten additional digits of the mobile subscriber
identification number (MSIC) complete the IMSI. The HLR can be
implemented in the same network node as the MSC or as a stand-alone
database. If the capacity of a HLR is exceeded by the number of
subscribers, additional HLRs may be added.
26
Visitor Location Register (VLR):
The VLR acts as temporary storage location for subscription
information of the mobile subscribers, which are within a particular
MSC service area. It contains the relevant data of all modules currently
located in a serving GSMC. Each MSC has one VLR and therefore,
MSC need not contact the HLR every time the subscriber uses a service
or changes its status. The temporary data of VLR is slightly different
from the permanent data found in the HLR. For example, the VLR
contains the temporary mobile subscriber identity (TMSI). Use of TMSI
in place of IMSI prevents the transmission of the IMSI via the air-
interface and it protects the subscriber from high-technology intruders.
The VLR supports the (G) MSC during a call establishment and an
authentication procedure by furnishing data specific to the subscriber.
The data traffic in HLR is reduced due to presence of VLR, as HLR is
not addressed every time the subscriber uses a service. The purpose of
having two identical data in two different locations viz. HLR and VLR
is different. The HLR provides the GMSC with the necessary subscriber
data when a call is coming from the public network. The VLR, on the
other hand provides the host GMSC with the necessary subscriber data
when a call is coming from mobile station.
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Authentication Center (AUC):
The main function of the AUC is to authenticate the subscribers
attempting to use a network. In this way, it is used to protect network
operators against fraud. The AUC is a database connected to HLR,
which is provided with the authentication parameters, and ciphering
keys used to ensure network security.
Equipment Identity Register (EIR):
It is a database, which contains list of all valid mobile equipments on the
network. The mobile station is identified by the International Mobile
Equipment Identity of the mobile station. If MS is stolen and reported
or it is not an approved, then it is marked as invalid. The serial numbers
of all the mobile equipments which have been stolen or not usable in
the network due to defect in the hardware are available in the EIR.. This
enables the network to check the identity at each registration or call
setup of any mobile station. Based on the status of the IMEI,
accessibility to the network system is decided. The EIR concept is a
relatively a new security feature in the GSM system.
28
2.1.4 Operation and maintenance subsystem:
The operation and maintenance centre (OMC) has access to both the
(G)MSC and the BSC, handles error message coming from the network,
and control the traffic load of the BSC and the BTS. The OMC
configures the BTS via the BSC and allows the operator to check the
attached components of the system. As the cells become smaller and the
number of base stations increases, it will not be possible in the
future.4
2.1.5 Interfaces:
The BTS is connected to a BSC by a link (E1 link, Euro-1 link) called
Abis interface. The Abis interface is a channelized time-division
multiplexing (TDM) link in which each user connection typically
requires 8 Kbps depending on the modulation scheme. Additional E1
links are provided from the BTS to the BSC to allow services offered by
GPRS and EDGE, such as web browsing and file download. The E1
links cannot be bundled. The E1 links for GPRS and /or EDGE do not
_________________________ 4 Cellular Operator Association of India. (2013). GSM System and Cellular Architecture. New- Delhi: Author. Retrieved from http://www.coai.com/ technology.php
29
change the basic architecture of the BTS or the protocol requirement on
an E1. The BSCs are physically connected via dedicated /leased lines or
microwave link to the MSC. The interface between a BSC and a MSC is
called A interface.
2.2 Network Availability, Reliability and Survivability:
There is increase in complexity, scale, and speed of communication
networks. Network performance under failures has become a great
concern in the telecommunication industry. A failure in the network
may significantly reduce the capability of the communication network to
efficiently deliver service to the users. Therefore, communication
network must be reliable. Availability is one of the most important
measures in reliability theory. Many faults occurred in individual items
of apparatus of the network. Faults are occurred in various subsystems
of the wireless network. The network switching subsystem and
operation & maintenance subsystem are fault tolerant because of the
distributed nature of its control. The faults occurred in individual items
of these two subsystems have little effect on the overall quality of
service. The fault liability of the base station subsystem particularly in
the base transceiver station is very high. Base stations are very often
30
compelled to go to down condition due to certain reasons like failures in
the equipments of the BTSs, the media connecting the BTSs to BSC
(Abis interface link) and inadequate supply of electrical energy at the
base stations. In BSNL Manipur, on average, forty percent of the total
downtime period of the BTS is due to media & equipments failures and
the rest sixty percent is due to non-availability of adequate energy. In
order to ensure maximum availability hours, the fault must be diagnosed
and rectified and there must be adequate supply of electrical energy at
the base stations. If there is longer the mean time to failures (MTTF) and
the shorter mean time to restore (MTTR), then there will be greater the
proportion of time for which the network provides service. This
proportion is called the availability of the network.5
Availability =
The availability gives the probability that the equipment will operate
correctly when required. The probability that the equipment/network
will not operate is called unavailability.
Unavailability = 1 – availability
__________________________ 5 Flood, J.E. (2011). Telecommunication Switching, Traffic and Networks. New-Delhi: Pearson Education, p. 192.
31
Therefore, availability tells us the expected time the entire system is up,
as opposed to down.
Reliability:
Reliability is defined as the network’s entire ability to perform a
designated set of functions under certain conditions for a specified
operational time.6 Reliability describes the chance that a network will
not fail over a specified period of time. A network component is said to
fail when it ceases to perform its intended functions. Y. Chen (2006)
asserts, “Component reliability can be expressed in the following
equation” (as cited in E.E. Lewis, 1987).
R(t) = e−λt = e−t/MTTF
where, λ is expected failure rate and MTTF is the expected mean time
between failures for that component type. If the time period of
interest is reasonably short, MTTF is assumed to be constant.
__________________________ 6 Preeti, Rastogi. (2005). Assessing Wireless Network Dependability Using Neural Networks
(Master’s thesis, Ohio University, USA). p.19. Retrieved from https://etd.ohiolink.edu /ap:0:0: APPLICATION_ PROCESS=DOWNLOAD_ETD_SUB DOC_ ACCNUM:::F1501_ID: ohiou1129134364,inline
32
Survivability:
Network survivability reflects the ability of a network to continue to
function during and after failures. Y. Chen (2006) asserts, “Network
survivability is defined as the ability of a network to provide services to
most customers under partial failures” (as cited in A. Snow, 1998). In
spite of redundancy in the network, failures that impact large number of
customers under some circumstances still occur. The level of a
network’s survivability is critical to a service provider’s ability to satisfy
most of its customers when disturbance occur (such as those due to
component failures). Thresholds are often applied to declare when a
network is in a “non-survivable” state.7
2.3 Telecommunications Traffic:
2.3.1 Unit of Traffic
Traffic engineering analysis enables one to determine the ability of a
telecommunication network to carry a given traffic at a particular loss
concepts equally apply to cellular networks. In designing an industrial
_________________________________________
7 Chen, Yachuan. (2006). Episodic Perspective of Wireless Network Dependability (Master’s Thesis, Ohio University, USA), p.18. Retrieved from https://etd.ohiolink.edu/ap:0:0: APPLICATION_
PROCESS= DOWNLOAD_ETD_SUB_DOC_ACCNUM::: F1501_ID:ohiou1142279334,inline
33
plant, decision is made on the basis of the its size which can produce
desired throughput. For example, for an oil refinery, this is the number
of barrels per day. In a machine shop, it is the number of piece parts per
day. In telecommunications system, the traffic engineering was initially
conceptualized for design of telephone switches and circuit switching
networks. The number of calls, which is handled by the switch or the
network, is the traffic. In telecommunications, the traffic determines the
number of trunk to be provided. The trunk is a term used to describe any
entity that will carry one call. Trunking is an arrangement of trunks and
switches within a telephone exchange. Observation made on the number
of calls in progress for few minutes on a large telecommunications
system, such as a telephone exchange or a transmission route, reveals
that the number of calls varies in a random manner, as individual calls
begin and end. If this random variation is smoothed out by taking a
running average, the number of calls in progress is found to vary during
the day. For example, few calls are observed during night. However, the
number of calls rises as people go to work. Number of calls reaches a
maximum by the middle of the morning, but drops again during
lunchtime. There is increase of calls in the afternoon. It decreases as
34
people go home from work and it has a further peak in the evening as
people make social calls.
As the traffic determines the number of trunks to be provided, the
trunks must be sufficient for the busiest time of the day. In traffic
engineering, durations of one-hour intervals are chosen for measurement
of traffic and the time interval, which has highest traffic, is called the
busy hour. The busy hour may vary from exchange to exchange
depending on the location and the community interest of the subscribers.
In addition, it may show seasonal, weekly and in some places even daily
variations. Besides these, unpredictable events such as stock market
activity, weather, natural disaster etc. may create peak traffic and busy
hour. In telecommunications, some call attempts are not materialize into
actual conversation due to reasons such as called line busy, no answer
from the called line, and blocking in the truck groups or the switching
centers. A call attempt is said to be successful or completed if the called
party answers. Call completion rate (CCR) is defined as the ratio of the
number of calls to the number of call attempts. The average number of
calls attempts during the busy hour is called the busy hour call attempts
(BHCA). It is an important parameter in deciding the processing
capacity of the common control or a stored program control system of
35
an exchange. The CCR parameter is used in dimensioning the network
capacity particularly in trunk and switch pertaining to landline
exchange. The telecommunications network or the switch must be able
to handle the busy hour call attempts. The capacity of the trunk is
determined on the basis of the BHCA. The traffic load on a given
network may be on the local switching unit, interoffice trunk lines or
other common subsystems. The traffic on the network is measured in
terms of occupancy of the network system and such a measure is called
the traffic intensity, which is defined as ratio of the period for which the
system is occupied to the total period of observation. For example, a
radio channel that is occupied for thirty minutes during an hour carries
0.5 Erlangs of traffic. The period of observation is generally taken as
one hour. The ratio, which is a dimensionless quantity, is used as unit of
traffic intensity and it is called erlang (E) to honor the Danish pioneer of
traffic theory.
The average number of calls in progress on a trunk group is
depended on both the number of calls which arrive and their durations.
The duration of a call is called its holding time because it holds a trunk
for that time. Traffic is sometimes expressed in terms of hundreds of
36
call seconds per hour (CCS). Since an hour contains 3600 seconds, 1
erlang = 36 CCS.
Therefore, traffic by a group of trunk is given by:
A =
where A = traffic in erlangs
C = average number of call arrivals during time T
h = average holding time
if h is expressed in seconds and T is taken as one hour i.e. 3600
seconds, then, traffic is given by:
A =
… 2.1
2.3.2 Mathematical Model of Traffic:
The mathematical model of traffic offered to telecommunications
systems is built up based on the following assumptions:
- Pure-chance traffic
- Statistical equilibrium
The call arrivals and call terminations are taken as random events under
the assumption of the pure-chance traffic. Individual user does not make
calls at random; however, the traffic in a telecommunications network is
37
the aggregate of the traffic generated by a large number of individual
users connected to the network. The total traffic generated by a large
number of users is observed to behave as if calls were generated at
random; hence, telecommunications traffic is characterized as a random
process. If call arrivals are independent random events, their occurrence
is not affected by previous calls. The traffic is therefore sometimes
called memoryless traffic.
The assumption of random call arrivals and terminations leads to the
following results:8
1. The number of calls arrivals in a given time has a Poisson
distribution, i.e.:
P(x) = ! e-µ … 2.2
where x is the number of call arrivals in time T and µ is the mean
number of call arrivals in time T. For this reason, pure chance
traffic is also called Poissonian traffic.
2. The intervals, T, between the call arrivals are the intervals
_________________________________ 8 Flood, J.E. (2011). Telecommunication Switching, Traffic and Networks. New-Delhi:Pearson Education, p. 93.
38
between independent random events and these intervals have a
negative exponential distribution, i.e.:
P( T ≥ t ) = e / … 2.3
where 푇 is the mean interval between call arrivals.
3. Since the arrival of each call and its termination are independent
random events and have a negative exponential distributions, i.e.:
P( T ≥ t) = e / … 2.4
where h is the mean call duration (holding time).
The assumption that call termination are random may seem odd, because
it implies that a call is as likely to end if it has just started as if it has
been going on for a long time. However, in practice, some calls are short
and others are long, with the result that the distribution of holding times
is observed to fit the negative exponential distribution.
The assumption of statistical equilibrium means that the
generation of traffic is a stationary random process, i.e. probabilities do
not change during the period being considered. Consequently, the mean
number of calls in progress remains constant.
39
2.3.3 Lost-call systems and grade of service:
Theodore (2012) defined Grade of Service as a measure of congestion,
which is specified as the probability of a call being blocked (for Erlang
B) or the probability of call being delayed beyond a certain amount of
time (for Erlang C). Cellular radio systems rely on trunking to
accommodate a large number of users in a limited radio spectrum. A
small number channels in a cell are shared by many users by providing
access to each users on demand. In a trunked radio system, each user is
allocated a channel on a per call basis, and upon termination of call, the
previously occupied channel is immediately returned to the pool of
available channels. In the trunking theory, a fixed number of channels or
circuits accommodate large number of random users. This principle is
used in designing cellular radio systems. There is trade-off between
available channels and the likelihood of a particular user finding that no
circuits are available during the peak calling time. If the occupation of
the channels of the trunk increases with the increase of landing to the
trunk by users, then there is likely that all channels will be busy for a
particular user. In the trunk, when all circuits/channels are already in
use, the user who tries to access the network is blocked or denied to
access the system.
40
The grade of service (GOS) is a measure of the ability of a user to
access a trunked system during the busiest hour. The grade of service is
a benchmark used to define the desired performance of a particular
trunked system by specifying a desired likelihood of a user obtaining
channel access given a specific number of channels available in the
system. Based on the desired GOS, the capacity for proper allocation of
channels is to be estimated while designing the trunking system.
Erlang followed the following assumptions in determination of
the grade of service (i.e. the loss probability) of a lost-call system having
N trunks, when offered traffic A, as shown in Figure 2.2.
- Pure chance traffic
- Statistical equilibrium
- Full availability
- Calls which encounter congestion are lost.
Figure 2.2: Lost-call system (Flood J.E., 2011)
41
In this system, the pure-chance traffic, which implies that the call
arrivals and call terminations are independent, and the statistical
equilibrium, which implies that probabilities do not change are assumed.
Full availability means that every call that arrives can be connected to
any outgoing trunk which is free. The switch that handles the incoming
calls must have sufficient outlets to provide access to every outgoing
trunk.
The lost-call assumption implies that any attempted call which
encounters congestion is immediately cleared from the system. When
this happens, the user is likely to make another attempt shortly
afterwards. Thus, the offered during the busy hour is slightly greater
than it would have been if there were no congestion. It is assumed that
the traffic offered is the total arising from all successful and
unsuccessful calls. The Erlang B formula determines the probability that
a call is blocked and is a measure of the GOS for a trunked system
which provides no queuing for blocked calls. The Erlang B formula is
given by
Pr[blocking] = !
∑!
= GOS … 2.5
42
where N is the number of trunked channels offered by a trunked radio
system and A is the total offered traffic.9
____________________________________ 9 Theodore, S. Rapport. (2012). Wireless Communications, Principles and Practice, 2nd Edition. New Delhi: Pearson Education, p. 79.
43
Source: http://fetweb.ju.edu.jo/staff/ee/mhawa/728/erlang.pdf
Table 2.1: Capacity of Erlang B System
44
While it is possible to model trunked systems with finite users,
the resulting expressions are much more complicated than the Erlang B
result and the added complexity is not warranted for typical trunked
systems, which have users that outnumber available channels, by orders
of magnitude. Furthermore, the Erlang B formula provides a
conservative estimate of the GOS, as the finite user results always
predict a smaller likelihood of blocking.10 The capacity of a trunked
radio system where blocked calls are lost is shown in Table 2.1 for
various values of GOS and number of channels/servers.
2.4 Modeling and Simulation:
2.4.1 Modeling:
Modeling is tool for representation and models define the boundaries of
the system we want to simulate. Tayfur et al. ( 2007) asserts, “Modeling
is the enterprise of devising a simplified representation of a complex
system with the goal of providing predictions of the system’s
performance measures (metrics) of interest. Such a simplified
representation is called a model. A model is designed to capture certain
____________________________________ 10 Theodore, S. Rapport. (2012). Wireless Communications, Principles and Practice, 2nd Edition. New Delhi: Pearson Education, p. 79.
45
behavioral aspects of the modeled systems- those that are of interest to
the analyst/modeler – in order to gain knowledge and insight into the
system’s behavior” (as cited in Morris, 1967).
Models can assume a variety of forms:
- A physical model is a simplified or scaled-down object (e.g., scale
model of an airplane)
- A mathematical or analytical model is a set of equations or
relations among mathematical variables (e.g., a set of equations
describing the workflow on a factory floor).
- A computer model is just a program description of the system. A
computer model with random elements and an underlying
timeline is called a Monte Carlo simulation model (e.g., the
operation of a manufacturing process over a period of time).11
2.4.2 Simulation:
Simulation is a tool for managing change and it is an imitation of reality.
Simulation can be viewed as solution to both the off-line design and on-
line operational management problems. Simulation technique is
____________________________________ 11 Benjamin, Melamed., & Tayfur, Altiok. (2007). Simulation Modeling and Analysis with Arena. Burlington, USA: Elsevier Inc., p. 2.
46
considered as a valuable tool because of its wide area of application. It
can be used to solve and analyze large and complex real world
problems. It is a representation of reality through the use of a model or
other device which will react in the manner as reality under a given set
of conditions. It is also defined as the use of a system model that has the
designed characteristics of reality in order to produce the essence of
actual operation.12 Prem K. Gupta et al, (2009) asserts, “According to
Shanon simulation is the process of designing a model of the real system
by conducting experiments with this model for the purpose of
understanding the behavior of the operation of the system”.
Many important managerial decision problems are too intricate to
be solved by mathematical programming and experimentation with the
actual system, even if possible, it is too costly and risky. Simulation
offers the solution by allowing experimentation with the model of the
system without interfering with the real system.13 Policy decisions can
be made much faster by knowing the options well in advance and by
reducing the risk of experimenting in the real system.14 Sterwart
_______________________________ 12 Prem, K. Gupta., & Hira,D.S.(2009).Operations Research. New-Delhi:S.Chand & Co. Ltd, p.1113. 13 op. cit. Gupta et al. 14 Jaisankar, S. (2006). Quantitative Techniques for Management. New-Delhi: Excel Books, p. 285.
47
Robinson (2004) asserts, “Ideas which can produce considerable
improvements are often never tried because of an employee’s fear of
failure” (as cited in Gogg and Mott, 1992). With a simulation, however,
ideas can be tried in an environment that is free of risk. This can only
help to encourage creativity in tackling problem situations.15 Simulation
enables the successful use of organizational improvement programs such
as Six Sigma. The activities of define, measure, analyze, improve, and
control depend on the earnest participation of everyone involved to
manage quality. In particular, the last three (analyze, improve & control)
revolve around identification of root causes, coming up with new
policies and practices, and putting controls in place to keep quality high.
Clearly, simulation can play the important role of reducing the risk of
change and managing change.16
Simulation has broad range of capabilities. By definition, these all
involve reproducing or projecting the behavior of a modeled system.
Computer-based simulations can involve everything from simple
_______________________________ 15 Stewart, Robinson. (2004). Simulation: The Practice of Model Development and Use. West Sussex, England: John Wiley & Sons, Ltd. 16 Barnett,M.W. (2003). Modeling & Simulation in Business Process Management. Gensym Corporation. Retrieved from http: //bpt.abudiconsulting.com/bpt/wp-content/ publicationfiles/11-
03%20WP% 20Mod%20Simulation%20of%20BPM%20-20Barnett-1. pdf
48
addition of a few numbers to intensive computations. Models for
simulation can be classified along four distinct dimensions: Systems of
Interest, Visibility, Probability, and Dynamics. The probability model
can be
- Probabilistic, that is, a single set of inputs that results in many
possible outputs—the outputs exhibit variations that are
described using statistics, or
- Deterministic, that is, the same set of inputs results in the same set
of outputs; the outputs are casually determined by preceding
events.17
Probability plays an important role in simulation just as it does in real
life. Models of reasonable size and complexity exhibit a set of possible
behaviors that, in general, are unknown unless the model is simulated.
Models also have validity constraints that identify when they are good
representations of the real world and when they contradict or
incompletely describe the real system. In order to understand the range
of possible behaviors, it would be useful to simulate the model under all
possible conditions. However, this is impractical, except for the simplest
_______________________________ 17 Barnett,M.W. (2003). Modeling & Simulation in Business Process Management. Gensym Corporation.
49
model. Instead, practitioners use techniques such as Monte Carlo
analysis.18 In this Monte Carlo method, the decision variables are
represented by a probabilistic distribution and random samples are
drawn from probability distribution using random numbers. The
simulation experiment is conducted until the required numbers of
simulations are generated. Finally, the best course of action is selected
for implementation. The significance of Monte Carlo Simulation is that
decision variables may not explicitly follow any standard probability
distribution such as Normal, Poisson, Exponential, etc. The distribution
can be obtained by direct observation or from past records.19
2.4.3 Procedure for Monte Carlo Simulation:20
1. Establish a probability distribution for the variables to be
analyzed.
2. Find the cumulative probability distribution for each variable.
3. Set Random Number intervals for variables and generate random
numbers.
_______________________________ 18 Barnett,M.W. (2003). Modeling & Simulation in Business Process Management. Gensym Corporation 19 Jaisankar, S. (2006). Quantitative Techniques for Management. New-Delhi: Excel Books, p.285. 20 Ibid., p. 286.
50
4. Simulate the experiment by selecting random numbers from
random numbers tables until the required numbers of simulations
are generated.
5. Examine the results and validate the model.
2.4.4 Analytical Versus Simulation Modeling:
A simulation model is implemented in a computer program. It is
generally a relatively inexpensive modeling approach, commonly used
as an alternative to analytical modeling. The tradeoff between analytical
and simulation lies in the nature of their “solutions,” that is, the
computation of their performance measures as follows:
1. An analytical model calls for the solution of a mathematical
problem, and the derivation of mathematical formulas, or more
generally, algorithmic procedures. The solution is used to obtain
performance measure of interest.
2. A simulation model (Monte Carlo) calls for running (executing) a
simulation program to produce sample histories. A set of statistics
computed from these histories is then used to form performance
measure of interest.21
_______________________________
21 Benjamin, Melamed., & Tayfur, Altiok. (2007). Simulation Modeling and Analysis with Arena. Burlington, USA: Elsevier Inc., p. 2.
51
The choice of analytical approach versus simulation is governed by
general tradeoff. For instance, an analytical model is preferable to a
simulation model when it has a solution, since its computation is
normally much faster than that of its simulation model counterpart.
Unfortunately, complex systems rarely lend themselves to modeling via
sufficiently detailed analytical models. Occasionally, though rarely, the
numerical computation of analytical solution is actually slower than a
corresponding simulation. In the majority cases, an analytical model
with a tractable solution is unknown, and the modeler resorts to
simulation. When the underlying system is complex, a simulation
model is normally preferable, for several reasons. Another way to
contrast analytical and simulation models is via the classification of
models into descriptive or prescriptive models. Descriptive models
produce estimates for a set of performance measures corresponding to a
specific set of input data. Simulation models are clearly descriptive and
in this sense serve as performance analysis models. Prescriptive models
are naturally geared toward design or optimization (seeking the optimal
argument values of a prescribed objective function, subject to a set of
constraints). Analytical models are prescriptive whereas simulation is
not. More specifically, analytical methods can serve as effective
52
optimization tools, whereas simulation-based optimization usually calls
for an exhaustive search for the optimum.22
2.4.5 Discrete-Event Simulation:
The majority of modern computer simulation tools implement a system
worldview, called the discrete-event simulation paradigm. In this system
worldview, the simulation model possesses a state at any point in time.
The state trajectory over time is abstracted as a piecewise-constant
function, whose jumps (discontinuities) are triggered by discrete events.
More simply, the simulation state remains unchanged unless a
simulation event occurs, at which point the model undergoes a state
transition. The model evolution is governed by a clock and a
chronologically ordered event list. Each event is implemented as a
procedure (computer code) whose execution can change state variables
and possibly schedule other events.23
2.5 Concepts of Economic Growth and Productivity:
2.5.1 Economic Activity and Concept of Productivity:
Business is an economic activity that involves the task of adjusting the
____________________________________ 22 Benjamin, Melamed., & Tayfur, Altiok. (2007). Simulation Modeling and Analysis with Arena. Burlington, USA: Elsevier Inc., p. 3. 23 op.cit. Benjamin et at. p. 4.
53
means (resources) to the ends (targets), or the ends to the means. An
economic activity may assume different forms such as consumption,
production, distribution, and exchange. The nature of business differs,
depending upon the form of economic activity being undertaken and
organized. The phenomenon of productivity is described as part of
economic activity and the concept of productivity has close relationship
with concepts like profitability, economic growth, efficiency, surplus
value, quality, performance, partial productivity, need etc.24
Productivity is based on the economics of the firms and it is an
important factor for evaluation of economic growth of an industry or a
nation. It is also considered as one of the major performance criteria for
evaluating a production system. It is a measure of output from a
production process, per unit input and it may be conceived of as a metric
of the technical or engineering efficiency of production.
Though the concept of productivity is sometimes considered as
synonymous with the efficiency, there is clear distinction between the
two. The ratio between the production of a given commodity or service
measured by volume, and one or more of the corresponding input
____________________________________ 24 Saari, Seppo. (2006). Productivity Theory and Measurement in Business. Paper presented at the European Productivity Conference, Espoo, Findland., p. 1. Retrieved from http://www.
mido.fi /index_tiedostot/Productivity_EPC2006_Saari.pdf
54
factors, also measured in volume is termed as productivity whereas
efficiency, unlike productivity, is expressed not in absolute, but in
relative terms. It is the ratio of actual output that should be obtained with
those resources in the same time period. The relation between an
individual input factor and production is termed as productivity of the
individual factor. However, when the overall productivity of an
organization is measured, it is called efficiency. It is thus obvious that
the term ‘efficiency’ has a wide coverage, because it is not concerned
with the productivity of a single input factor alone, but is concerned
with the overall productivity of all the input factors.25
Business firms being economic units may undertake different
types of activities such as manufacturing, trading, transport, banking,
service etc. with the motivational objective of profit maximization in the
long run. Profit is essentially “a surplus value” – the value of outputs
in excess of the values of the inputs or the surplus of revenue over the
cost. Profitability is therefore distinct from the metrics of productivity,
and profitability addresses the difference between the revenues obtained
____________________________________ 25 Antony, M.T. (1992). Efficiency in Central Public Sector Enterprises in Kerala: An Analysis of
Capacity Utilization, Profitability and Productivity (Ph.D Thesis, Cochin University of Science and Technology, Cochin, Kerala). Retrieved from http://dyuthi.cusat.ac.in/xmlui/bitstream/handle/purl/1597/Dyuthi-T0073.pdf
55
from output and the expenses associated with the consumption of inputs.
Profitability is regarded as an index of efficiency and management guide
to greater efficiency though it is not synonymous with efficiency. No
doubt, profitability is an important yardstick of efficiency of an
enterprise, but the extent of profitability cannot be taken as a final proof
of efficiency.
The basic feature of the behavior of the economic activity is the
interest of maximization of the output at minimal sacrifice in input. The
efficiency, which is typical of economic activity, speaks about the
relation between producing a value and sacrifices made in doing so.
Hence, efficiency is at issue when the required sacrifices are being
balanced against the value produced. Since efficiency is a general
concept related to economic activity, it needs to be given a precise name
and a formula case by case. Productivity and profitability are typically
such specified concepts of efficiency.26
A business firm is essentially a transformation unit. The idea of
the transformational process is to produce values, which is larger than
____________________________________ 26 Saari, Seppo. (2006). Productivity Theory and Measurement in Business. Paper presented at the European Productivity Conference, Espoo, Findland., p. 1. Retrieved from http://www.
mido.fi /index_tiedostot/Productivity_EPC2006_Saari.pdf
56
the sacrifices made to produce them. The surplus value stated above is
the relation or the difference between the produced value and sacrifice
made. The ability of the transformational unit to perform its task is its
performance, which is further depended on its quality and quantity.
Performance improvement takes place by developing the quality and
increasing the quantity as well as by evolving the use process. The
quality is the characteristics of the transformational unit (tool). Both the
quality and quantity are usually developed on the basis of the latest
know how and experience, and the work is carried out by means of
investment and development projects. The use process of tools evolves
over the time through learning . Production is a process of combining
various immaterial and material inputs of production so as to produce
tools for consumption. The way of combining the inputs of production
in the process of making output is called technology and it can be
depicted mathematically by the production function, which describes the
input and output. The production function is the measure production
performance.27 The production function is really an engineering concept
that is devoid of economic content. That is, it simply relates
____________________________________ 27 Saari, Seppo. (2006). Productivity Theory and Measurement in Business. Paper presented at the European Productivity Conference, Espoo, Findland., p. 2. Retrieved from http://www.
mido.fi /index_tiedostot/Productivity_EPC2006_Saari.pdf
57
output and input rates. The production function can be stated in the
general form of an equation:
Q = f (K, L)
where Q, the units of output, is a function of the quantity of two inputs
with K indicating units of capital , and L indicating units of labor. For
simplicity purpose, it is assumed that all inputs or factors of production
are grouped into two broad categories, labor (L) and capital (K) in this
equation. This function defines that the maximum rate of output (Q) per
unit of time obtainable from a given rate of capital and labor input.
Output may be physical units or it may be intangible. The production
function does not yield information on the least-cost capital-labor
combination for producing a given level of output nor does it reveal the
output rate that would yield maximum profit. The function only shows
the maximum output obtainable from any or all input combinations.
Prices of the inputs and price of output must be used with the production
function to determine which of the many possible input combinations is
best, given the firm’s objective.
58
2.5.2 Cobb-Douglas Production Function:
Although a variety of functional forms have been used to describe
production relationship, Cobb-Douglas model is one of the popular,
simplest, and appropriate production function that has been employed
for about a hundred years. Therefore, based on the conceptual
framework, this model is employed in analyzing productivity in this
research work. The general form of Cobb-Douglas function is expressed
as:
Q = A Kα Lβ
where α, and β are constants (output elasticity) that, when estimated,
describe the quantitative relationship between the inputs (K- capital
input and L- labor input) and output (Q). A is defined as the total factor
productivity (a constant parameter).
Output elasticity measures the responsiveness of output to a
change in levels of either labor or capital used in production. For
example, if α = 0.15, a 1% increase in labor would lead to
approximately a 0.15% increase in output.
Further, if:
α + β = 1,
59
the production function has constant returns to scale. That is, if L and K
are each increased by 20%, Q increases by 20%. If
α + β < 1,
returns to scale are decreasing, and if
α + β > 1
returns to scale are increasing.
The Cobb-Douglas function does not lend itself directly to
estimation by the regression methods because it is a nonlinear
relationship. Technically, an equation must be a linear function of the
parameters in order to use the ordinary least-square regression method
of estimation. However, a linear equation can be derived by taking
logarithm of each term. That is,
log Q = log A + α log K + β log L
A linear relationship can be seen by setting,
Y = log Q, A* = log A, X1 = log K, X2 = log L
and rewriting the function as
Y = A* + αX1 + βX2
The function can be estimated directly by the least- square regression
technique and the estimated parameters used to determine all the
60
important production relationships. The antilogarithms of both sides can
be taken, which transforms the estimated function back to its
conventional multiplicative form.
2.5.3 Economic growth and productivity:
An economic community achieves economic growth when there is
increase in production. The mechanism of economic growth can be
described with the help of production function. The production function
is a simple description of the mechanism of economic growth.
Economic growth is created by two factors so that it is appropriate to
discuss about the components of growth. These components are an
increase in production input and an increase in productivity.28
Economic growth process is illustrated in Figure 2.3. The increase
in production output is represented by T2-T1 and while changing values
from T1 to T2, we have observed that there is increase in input value
from P1 to P2. The lines 1 and 2 represent graphs of two production
functions. The increase of output from T1 to T2 is distinguishable by
two factors viz. (1) the growth caused by an increase in production
____________________________________ 28 Saari, Seppo. (2006). Productivity Theory and Measurement in Business. Paper presented at
the European Productivity Conference, Espoo, Findland., p. 2. Retrieved from http://www. mido.fi /index_tiedostot/Productivity_EPC2006_Saari.pdf
61
input, and (2) the growth caused by an increase in productivity. The
growth caused by an increased input is determined by moving along the
production function for a respective input increase, i.e. from Value P1 to
Value P2. Characteristic of the growth effected by an input increase is
that the relation between the output and input remains unchanged. An
increase in output means a shift of the production function
simultaneously with a change in the output/input relation. In other
words, the output growth corresponding to a shift of the production
function is generated by the increase in productivity.29
OUTPUT VOLUME OUTPUT VOLUME Growth caused by productivity increase T2 Growth caused by Increase of Input volume INPUT VOLUME
2 T2 1 T1 P1 P2
____________________________________ 29 Saari, Seppo. (2006). Productivity Theory and Measurement in Business. Paper presented at the European Productivity Conference, Espoo, Findland., p. 2. Retrieved from http://www.
mido.fi /index_tiedostot/Productivity_EPC2006_Saari.pdf
Figure 2.3: Components of Economic Growth (Saari 2006)
62
The output growth corresponding to a shift of production function
demonstrates that an increase in productivity is characterized by a shift
of the production function and a consequent change to the output/input
relation. The formula of total productivity is normally written as
follows:
Total productivity =
2.5.4 Total Factor Productivity:
The production process involves two or more inputs working jointly to
create output; it can be difficult to measure changes in the productivity
of any one factor over time. A common mistake in measurement of
productivity is to simply divide output by input at two points in time to
ascribe the difference in the ratio as an increase in the productivity on
that input. Productivity is generally defined as a measure of the
efficiency of the transforming inputs into outputs. The ratios of output to
particular inputs are termed as partial productivities, whereas, the ratio
of output to a weighted sum of all the inputs used in the production
process is defined as Total Factor Productivity (TFP). The use of a
total factor productivity approach provides a meaningful measure of the
joint productivity of the inputs. Total factor productivity is given by
63
TFP =
where, r and w are input prices in the base year.
TFP can be measured from different methods.
Method of Kendrick:
Kendrick presented the special way to measure the TFP.
TFP =
Q1= Output with constant value or the real value added. K= Real
Capital. L= Number of persons or working hours of labors. α and β are
defined as the portions of labor and Capital in production or value
added. This research uses the method of Kendrick in measurement of the
TFP of the wireless network.
Method of Dujea:
Dujea presented the following method.
TFP =
Qt = output with constant value or the real value added. K = real capital.
L= number of persons or working hours of labors. α and β are defined as
the portions of labor and capital in production or value added. In this
64
approach α + β =1. So, by measuring one of the elasticity, the other one
will be calculated.
Method of Solow:
Solow presented the following method:
TFPt = Qt −αLt− βKt
According to the above equation, if labor and capital stay constant, the
output will be changed only by Total Factor Productivity. By taking
logarithm from the Dujea model and then using differentiation, Solow
approach will be achieved.
