Post on 22-Oct-2014
Chapter Three
The Cellular Concept:
System Design
Fundamentals
1
BY : Amare Kassaw
Goal of the Chapter
In cellular system, the available radio spectrum is limited
E.g., because of regulatory issues
Hence, the number of simultaneous call supported is limited
How to achieve high capacity (or support simultaneous calls) at
the same time covering very large areas?
Frequency reuse by using cells
Overview system design fundamentals on cellular communication
Cell formation and the associated frequency reuse, handoff, and
power control
2
Lecture Outlines
Introduction
Cellular Concept & Frequency Reuse
Channel Assignment Strategies
Handoff Strategies
Interference and System Capacity
Trunking and Grade of Services
Summary
3
Used Acronyms • BS: Base station • MS: Mobile station • MSC: Mobile switching center • GOS: Grade of services • CCI : Co-channel interference • ACI: Adjacent channel interference
4
Introduction Conventional Mobile Radio System and its Limitations
Single high power transmitter and large antenna towers/masts
Large coverage area/larger size radios with large batteries
Limited number of channels
Poor quality of service
Still in use for some public/private organizations
5
The coverage area called tower footprint of these towers was
theoretically circular in shape with radius around 50 km.
As long as cities being covered were far away from each other, no
interference occurred between the transmissions in different
cities.
6
The assigned spectrum (40 MHz or more) was used in every city being
covered.
The bandwidth for full duplex transmission would give a total of 60 kHz
per user
Thus total number of users who can call or receive calls at the same time
in any city was around 660 users only.
For a large city(with 10,000,000 residents for example) this is extremely
low and the system would get congested so easily.
7
Due to the large distance between the MS and the BS (up to 50
km or more), mobile phones had to transmit high powers.
This results in the need for large batteries and therefore phones
were large in size and inconvenient.
So, cellular system with frequency reuse is the solution to avoid
the problem of spectral congestion , capacity and power budget.
8
The Cellular System
High capacity is achieved by limiting the coverage area of each
BS to a small geographic region called a cell
Single, high power transmitter (large cell) are replaced with
many low power transmitters (small cells)
A portion of the total number of channels is allocated to each cell
or BS
Available group of channels are assigned to a small number of
neighbouring BS called cluster
Near by BS are assigned d/t groups of channels to minimize
interference9
Cellular System- Architecture
10
Same channels (frequencies/timeslots/codes) are reused by
spatially separated base stations
Reuse distance and frequency reuse planning.
A switching technique called handoff enables a call to proceed
from one cell to another
As demand (# of users) increases, the number of BS may be
increased to provide additional capacity
Smaller cells, e.g., Microcells, Picocell, Femtocell
Also cell sites in trucks to replace downed cell towers after
natural disasters, or to create additional capacity for large
gatherings(football games, rock concerts)11
Transmission power reduction => interference decreases
Typical power transmitted by the radios in a cell system
Base Station: Maximum Effective Radiated Power (ERP)
is100W, or up to 500 W in rural areas
Mobile Station: Typically 0.5 W , for CDMA transmit power
is lowered when close to a BS
12
The Cellular Concept The Cellular Idea
Divide the service area into several smaller Cells
Put at least as many towers as the # of cells and reduce the transmitter
power of each BS
Reuse the allocated frequency spectrum (channels) as many times as
possible avoiding interference
Gains but with Pains
Greater system capacity at the cost of large infrastructure
Optimal frequency spectrum utilization attained by making system
more complicated
User equipment design made smarter at the cost of circuit complexity
and processing power13
Frequency Reuse Example
14
The Cell Shape
Actual radio coverage area of cell is amorphous (irregular shaped)
Obtained by field measurements or by using prediction models
through computer simulation
This is known as footprints
(a) is theoretical coverage area and (b) measured coverage area
where red, blue, green, and yellow indicate signal strength in
decreasing order
15
All cells should have same shape and equal area
Circular (theoretical): If path loss was a decreasing function of
distance(say 1/dn) where d is the distance b/n BS & MS
16
17
When using hexagon to model coverage areas
Center-excited cell: BS depicted as being in the center of the cell
• Omni-directional antenna is used
Edge-excited cell: on three of the six cell vertices
• Sectored direction antenna is used
18
Geometry of Hexagons
Axes U and V intersect at 600
Assume unit distance is the distance between cell centers
If cell radius to point of hexagon is R, then
2Rcos 30o = 1 or R = 1/3 (Normalized radius of a cell)
To find the distance of a point P(u,v) from the origin, use XY to
U-V coordinate transformation as
19
Using this equation, to locate the co-channel cells, start from a
reference cell and move
i-hexagons along the U-axis and
j-hexagons along the V-axis
The distance, D, between co-channel cells in adjacent clusters is
given by
20
The number of cells in a cluster is given by
where i and j are non-negative integers
In real system , there are only certain cluster sizes and layouts
possible.
Typical values of N are 1, 3, 7, 12, …
21
Locating Co-channel Cells
Observation: The Geometry of the Hexagons is such that the
number of cells per cluster, N, can only have values such that
Hence to find out the nearest co-channel neighbours of a
particular cell, do the following
Move i cells in the U direction
Then turn 60 degree counter clockwise and move j cells in the
V direction
22
Example : N=7, i=2,j=1
23
Example : N=28, i=4, j=2
24
Frequency Reuse Principles
Let us assume a city of 10 Million mobile users
Let every user is allocated a radio spectrum for analog speech of
4kHz bandwidth
Thus the required bandwidth is 4 kHz * 10 Million users = 40
GHz!
Clearly impractical!
No other services possible using a radio transmission
Most of the spectrum will be unused most of the time
25
Cellular radio systems rely on intelligent allocation and reuse of
channels through out the coverage area
Available group of channels are assigned to a cluster
Same group of frequencies are reused to cover another cell
separated by a large enough distance,
• Hence a trade-off in the design is required
26
To understand the frequency reuse concept, consider a cellular
system which has a total of S duplex channels available for use
If each cell is allocated a group of k channels (k<S), and if the S
channels are divided among N cells into unique and disjoint
channel groups each have the same number of channels
The total number of available radio channels can be expressed as
S = kN
The N cells that collectively use the complete set of available
frequencies is called a cluster
27
If a cluster is replicated M times within the system, the total
number of duplex channels can be used as a measure of capacity
and is given
C =MS= MkN
The factor N is called the cluster size and is typically values are
1,3 , 7, 12,...
28
The value N is a function of how much interference a mobile or
BS can tolerate while maintaining a sufficient quality of
communications.
Smallest possible value of N is desirable in order to maximize
capacity over a given coverage area
The frequency reuse factor of a cellular system is given by 1/N
29
Effect of Cell Size Trade offs
Advantages of smaller cell size:
Higher M (more replications of cell cluster)
Higher system capacity
Lower power requirements for mobiles
Disadvantage of smaller cell size:
Additional base stations required
More frequent handoffs
Extra possibilities for interference
30
Effect of Cluster Size Trade offs
Each clusters have unique group of channels which are repeated
over clusters
Keeping cell size the same
Large N: weak interference but lower capacity
Small N: higher capacity, more interference, need to maintain
certain S/I level
• More clusters are required to cover area of interest,
• So capacity is directly prop. to replication factor for fixed area
• Results in larger co-channel interference
• May result in lower Quality of Service (QoS)31
System Design Examples
32
A total of 33 MHz bandwidth is allocated to a particular FDD Cellular Phone System. If the Simplex
Voice/Control Channel bandwidth is 25 KHz, Find the total # of Channels available per Cell if the
System uses (a) 4-Cell Frequency Reuse (b) 7-Cell Frequency-Reuse Plan. If 1 MHz out of the total
allocated bandwidth is used for Control Channels, determine an equitable distribution of the Control
and Voice Channels in each Cell in case of each Frequency-Reuse Plan.
Solution:Total allocated bandwidth = 33 MHz, Duplex channel bandwidth = 25x2=50 KHzTotal # of Available(Voice/Control) Channels = 33,000/50 = 660 Channels.
(a) N= 4, so total # of Channels/Cell = 660/4 = 165 Channels(b) N=7, so total # of Channels/Cell = 660/7 = 95 Channels In Case of 1 MHz bandwidth allocated for Control Channels, total # of Control Channels =
1000/50=20 Channels per Systems. Out of 660 Channels, 20 are used as Control and remaining 640 as Voice Channels.
(a) N=4, Each Cell can have 20/4=5 Control Channels and 640/4=160 Voice Channels. But, each Cell needs only one Control Channel, so, each cell will be assigned one Control Channel and 160 Voice Channel.
(b) N = 7, Each Cell can have 20/7 = 3 Control Channels and 640/7=91 Voice Channels[Plus 3 Extra], but it needs only 1 Control Channel, so, we can assign 4 Cells with 91 Voice Channels and one Control Channels, and 3 Cells with 92 Voice Channels and one Control Channels.
The Channel Assignment Strategies Objective: maximize the system capacity while minimizing the
interference A constrained optimization problem
Classification:Fixed Channel AllocationDynamic Channel AllocationHybrid Channel AllocationBorrowed Channel Allocation
Choice has impact on system performanceHandoffCall InitializationMSC Processing Load
33
Fixed Channel Assignment (FCA)
Each cell is allocated a predetermined set of voice channels.
Any call attempt within the cell can only be served by the unused
channels in that particular cell.
Any request for a handoff , if all channels of this candidate cell are
in use, will not be treated.
MS may have to wait, call can drop even
Probability of blocking is high.
34
Simple, but a busy cell will run out of channels before a neighbouring
cell
Service variations of fixed assignment strategy exit
System performance will be limited by the most crowded cell
Several solution to solve the problem: Borrowing Strategy Reserve Some Channels for Handoff
35
Borrowing channel assignment strategies
Modified from fixed channel assignment strategies.
A cell is allowed to borrow channels from a neighbouring cell if
all of its own channels are already occupied.
The MSC supervises such borrowing procedures and ensures
that the borrowing of a channel does not disrupt or interfere
with any of the calls in progress in the donor cell.
36
Dynamic Channel Assignment
Channels are not allocated to different cells permanently.
Each time a call request is made, the serving base station requests
a channel from the MSC.
To ensure a required QoS, the MSC allocates a given frequency if
that frequency is not currently in use in
The cell, or
In any other cell which falls within the limiting reuse distance,
i.e., channels in neighbouring cells must still be different
37
The MSC allocates a channel to the requested cell following an
algorithm that takes into account :
The likelihood of future blocking within the cell,
The frequency of use of the candidate channel,
The reuse distance of the channel, and
Other cost functions.
DCA requires the MSC to collect real-time data on channel
occupancy, traffic distribution, and radio signal strength
indications (RSSI) of all channels on a continuous basis.
38
Hence DCA
Reduces the call blocking probability and call drop
probability during hand off
Improves system Trunking capacity (traffic intensity/channel):
all channels are accessible by all cells
But adds the costs of storage and computational load on
MSC because
• MSC must collect real-time channel occupancy data
• Traffic distribution information
• Radio signal strength indications (RSSI) of all the channels
39
The Handoff Strategies
In a cellular network, the process to transfer the ownership of a
MS from a BS to another BS is termed as Handoff or Handover.
MSC facilitates the transfer
In general, handoff involves
Identifying the new BS
Allocation of voice and control signals to channels with the new
BS
Usually, priority of handoff requests is higher than call
initiation requests when allocating unused channels.
40
Handoffs must be performed
Successfully
As infrequently as possible, and
Must be imperceptible to the user
To meet these requirements, we must specify a minimum usable
signal level for acceptable voice quality at the base station
If the received power drops too low prior to handoff, the call
will be dropped so that users complain about dropped calls
41
Handover Indicator: The parameters to monitor to determine HO
occasion
RSSI: in ensemble average sense.
Bit Error Rate (BER)/Packet Error Rate (PER), more accurate.
By looking at the variation of signal strength from either base
station, it is possible to decide on the optimum area where handoff
can take place.
42
Once a particular signal level is specified as the minimum usable
signal for acceptable voice quality at BS receiver (normally b/n
- 90 dBm and -100 dBm), a slightly stronger signal level is used as
a threshold at which a handoff is made.
If Δ is too large: unnecessary handoffs may occur, burden on MSC
If Δ is too small: there may be insufficient time to complete a handoff,
calls may be loss or dropped.
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Example 1: Improper Handoff Situations
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Example 2: proper Handoff Situations
45
How to Prioritize Handoffs
Guard Channel Method
A fraction of the total available channels is reserved for
handoffs
In case of fixed channel assignment, it affects system capacity.
But good in case of dynamic channel assignment
Queuing Handoff Request Method
Any handoff request, if can not be tackled immediately, it will be
placed in a queue for sometime before the signal levels goes
below the minimum acceptable and it has to be dropped.
Does not guarantee 100% success for all handoff requests46
Handoff Styles
1. Network Controlled Handoff (NCHO)
Used in the 1st generation analog cellular systems
Here each BS constantly monitors signal strength from MS in its
cell.
Based on the measures, MSC decides if handoff is necessary or
not.
MS plays a passive role in process
Creates heavy burden on MSC
47
2. Mobile Assisted Handoff (MAHO)
Used in 2nd and above generation systems
MS measures received power from surrounding BS and report to
serving BS
Handoff is initiated when power received from a neighboring
cell exceeds current value by a certain level or for a certain period
of time
Faster since measurements made by MS
MSC doesn’t need to monitor the signal strength
• Simple burden on MSC
48
3. Hard Handoff: break before make
FDMA, TDMA (1G and 2G Systems)
The mobile has a radio link with only one BS at anytime.
Old BS connection is terminated before new BS connection is
made
4. Soft Handoff: Make before break
The CDMA system mobile has simultaneous radio link with more
than one BS at any time.
New BS connection is made before old BS connection is broken.
Mobile unit remains in this state until one base station clearly
predominates. 49
5. Intersystem Handoff:
Used for MS at the border of the system(home service provider’s
service area)
MSC of the serving cell talks to the MSC of the neighboring
system or vice versa to transfer the call.
Several issues should be resolved before handoff can take place
• Call type• Roaming is allowed or not• Compatibility issues or standards• User authenticity and call charges issues
50
Practical Handoff Problems Problem 1: Simultaneous traffic of high speed and low speed
mobiles.Small cell → high speed mobile → frequent handofflarge cell → Reduce capacity
Solution: Umbrella Cell - cell split or hierarchical cell structure
By using different antenna heights and different power levels,
it is possible to provide large and small cells which are co-
located at a single location.
Small cell for low speed mobileLarge cell for high speed mobileNeed strong detection and handoff control.
51
This concept minimizes the number of handoffs for high speed
users and provides additional micro cell channels for pedestrian
users
52
Problem 2: Cell Dragging
Caused by pedestrian users that provide a very strong signal to the
BS.
Often occurs in an urban environment when there is a line-of-
sight (LOS) radio path between the subscriber and the base station.
As the user travels away from the BS at a very low speed, the
average signal strength does not decay rapidly and the received
signal at the BS may be above the handoff threshold, thus a handoff
may not be made.
Creates a potential interference and traffic management problem.
Solution: Careful arrangement of handoff threshold and radio coverage
parameters.53
Interference and System Capacity What is Interference: unwanted signal which affects the speech
quality and system capacity
Sources of Interference includes:
Another mobile in the same cell
A call in progress in the neighboring cell
Other BS operating in vicinity using the same frequency band,
Some non cellular device/system leaking energy in the cellular frequency band.
Two major types of interference are:
Co-Channel Interference (CCI)
Adjacent-Channel Interference(ACI)54
It is a major Bottle Neck in system capacity: a trade off has to be
made between system capacity and information quality.
Interference in the voice channels causes crosstalk
A subscriber hears interference in the background due to an
undesired transmission
Interference in the control channels causes error in digital
signalling which causes
Missed calls
Blocked calls
Dropped calls55
Co-Channel Interference and System Capacity
Frequency reuse implies that in a given coverage area there are
several cells that use the same set of frequencies
These cells are called Co-channel cells, and the interference
between signals from these cells is called co-channel interference
Note that thermal noise caused by electronic components can be
overcome by increasing the signal to noise ratio (SNR)
But co-channel interference cannot be reduced by simply
increasing the carrier power of a transmitter.
Because an increase in carrier transmit power increases the
interference to neighbouring co-channel cells.56
57
To reduce co-channel interference, co-channel cells must be
physically separated by a minimum distance to provide sufficient
isolation due to propagation .
So, when the size of each cell is approximately the same, and the
BS transmit the same power, the co-channel interference ratio is
independent of the transmitted power and becomes a function of
the radius of the cell (R) and the distance between centres of the
nearest co-channel cells (D)
By increasing the ratio of D/R, the spatial separation between co-
channel cells relative to the coverage distance of a cell is
increased.58
Thus interference is reduced from improved isolation of RF
energy from the co-channel cell
Co-channel Reuse Ratio (Q): The spatial separation between co-
channel cells relative to the coverage distance of a cell.
For a hexagonal geometry, it is related to the cluster size N
A small value of Q provides larger capacity since the cluster size
N is small, whereas a large value of Q improves the transmission
quality, due to a smaller level of co-channel interference
59
Co-channel reuse ratio for some values of N
60
Hence there is capacity versus interference trade off
Co-Channel Signal to Interference Ratio
Let i0 be the number of co-channel interfering cells, then the
signal-to- interference ratio (S/I or SIR) for a mobile receiver
which monitors a forward channel can be expressed as
Where S is the desired signal power from the desired BS
Ii is the interference power caused by the i th interfering
co-channel cell BS
61
Propagation measurements in a mobile radio channel show that
the average received signal strength at any point decays as a
power law of the distance between a transmitter and receiver
The average received power Pr at a distance d from the
transmitting antenna is then
Where Po is the received power at a close-in reference distance
in the far-field and n is the path-loss exponent (mostly between 2 to 5)
62
Now consider the forward link where the desired signal is the
serving BS and the interference is due to co-channel BS.
If Di is the distance of the ith interferer from the mobile, the
received power at a given mobile due to the ith interfering cell will
be proportional to (Di)-n.
When the transmit power of each BS is equal and n is the same
throughout the coverage area, S/I for a mobile can be approximated
as
63
For simplicity, assume all interferers have equidistance, that is for
only the first layer of equidistant interferers
This relates S/I to the cluster size, and in turn determines the
overall capacity of the system
Puts a limit on how low we may set N
64
For a hexagonal cluster of cells with the MS situated at the edge
of the cell
Hence, as long as all cells are of the same size, S/I is
independent of the cell radius, R
65
Example
If a signal to interference ratio of 15 dB is required for satisfactory
forward channel performance of a cellular system, what is the
frequency reuse factor and the appropriate cluster size that
should be used for maximum capacity if the path loss exponent is
(a) n = 4 , (b) n = 3? Assume that there are 6 co-channels cells in
the first tier, and all of them are at the same distance from the
mobile. (Hint: First consider 7 cell reuse pattern and decide the
practical cluster size.
66
Adjacent Channel Interference
Interference resulting from signals which are adjacent in frequency
to the desired signal is called adjacent channel interference.
An interference arising from energy spill-over between two
adjacent channels.
Adjacent channel interference results from imperfect receiver
filters which allow nearby frequencies to leak into the pass band.
The problem can be particularly serious if an adjacent channel user
is transmitting in very close range to a subscriber's receiver.
67
This is referred to as the near-far effect, where a nearby
transmitter (which may or may not be of the same type as that
used by the cellular system) captures the receiver of the
subscriber.
Alternatively, the near-far effect occurs when a mobile close to a
BS transmits on a channel close to one being used by a weak
mobile.
The BS may have difficulty in discriminating the desired
mobile user from the close adjacent channel mobile.
68
Near-far effect: The adjacent channel interference is particularly
serious.
This occurs when an interferer close to the BS radiates in the
adjacent channel, while the subscriber is far away from the BS
The BS may not discriminate the desired mobile user from the
“bleed over” caused by the close adjacent channel mobile
Or, an interferer which is in close range to the subscriber’s
receiver is transmitting while the receiver receives from the
BS.
69
70
In practice, power levels transmitted by every subscriber are under
constant control by the serving BS
Each MS transmits with the smallest power necessary
In power control
Reduces the transmit power level of MSs close to the BS since
a high TX power is not necessary in this case
MSs located far away must transmit with larger power than
those nearby
Power control reduces out-of-band interference, prolongs battery
life, and generally reduces even co-channel interference on the
reverse channel71
However, power control requires well
Controlling a mobile means communication from the BS to
the mobile to inform it whether to increase or decrease its
power, which then requires data overhead
In CDMA systems, every user in every cell share the same radio
channel means a tight power control is required
The “near-far problem” is even more of a problem in CDMA
Need to reduce the co-channel interference
Reduced interference leads to higher capacity
72
ACI can be minimized through careful filtering and channel
assignments.
By keeping the frequency separation between each channel in a
given cell as large as possible, the adjacent channel interference
may be reduced considerably
Channels are allocated such that the frequency separation between
channels in a given cell is maximized.
73
If a subscriber is at a distance d1 and the interferer is d2 from the base station, then SIR (prior to filtering) is
Example:
Suppose a subscriber is at d1 = 1000m from the BS and an
adjacent channel interferer is at d2 = 100m from the BS
Assume: Path loss exponent is n = 3
The signal-to-interference ratio prior to filtering is then
Hence we should use a careful filtering to avoid this .
74
Trunking and Grade of Services
Trunking System: A mechanism to allow many user to share
fewer number of channels.
Not every user calls at the same time.
Penalty: Blocking Effect.
If traffic is too heavy, call is blocked!!
Small blocking probability is desired.
There is a trade-off between the number of available circuits and
blocking probability.
75
Trunking refers to sharing a fixed and small number of channels
among a large and random user community
Accommodating a large number of users in a limited radio
spectrum
Trunking exploits the statistical behaviour of users
Let U be number of users and C be number of channels
Each user requires a channel infrequently
So a dedicated channel for each user is not required
However, request for a channel happens at random times
So for any C < U, possibility of more requests than channels76
Trunking accommodates large & random users:
By providing access to each user on demand from a pool of
available channels
When a user requests service and if all channels are already in use,
the user is blocked or denied access to the system
In some systems, a queue may be used to hold the requesting users
until a channel becomes available
Upon termination of the call, the previously occupied channel is
immediately returned to the pool
Designing a trunked system, that can handle a given capacity at a
specific “grade of service”, requires Trunking and queuing theories.77
Terms Used in Trunking Theory
Setup time: The time required to allocate a radio channel to a requesting
user. Users request may be blocked or have to wait
Blocked Call: A call that cannot be completed at the time of request due
to congestion
Also called lost call => lost revenue, e.g., pick hours, holidays,
Holding Time(H): Average call duration in seconds
Depends on users and operator's tariff
Request (or call) Rate (λ): Average number of calls per unit time
Typically taken to be at the busiest time of day
Depends on type of users community: Office, residential, call center 78
Erlang: The amount of traffic intensity carried by a channel that
is completely occupied.
For example, a radio channel that is occupied for 30 minutes
during an hour carries 0.5 Erlangs of traffic.
Grade of Service (GOS): is a measure of the ability of a user to
access a trunked system during the busiest hour.
GOS is typically given as the likelihood that a call is blocked, or
the likelihood of a call experiencing a delay greater than a
certain queuing time.
79
Traffic Intensity(A): Measure of channel time utilization, which
is the average channel occupancy measured in Erlangs. This is a
dimensionless quantity and may be used to measure the time
utilization of single or multiple channels.
Load: Traffic intensity across the entire trunked radio system,
measured in Erlangs.
Grade of Service (GOS): A measure of congestion which is
specified as the probability of a call being blocked (Erlang B), or
the probability of a call being delayed beyond a certain amount
of time (Erlang C).
80
Trunking Efficiency: is a measure of the number of users which
can be offered a particular GOS with a particular configuration of
fixed channels.
The way in which channels are grouped can substantially alter the
number of users handled by a trunked system.
From Table 3.4, for GOS=0.01
10 trunked channels can support 4.46 Erlangs.
Two 5 trunked channels can support 2x1.36=2.72 Erlang.
10 trunked channels support 64% more traffic than two 5
channel trunks do.
81
Computation of GOS
Analysis
Average arrival rate(λ): Average number of MSs requesting
service (call request/time)
82
Average hold time(H): Average duration of a call (or time for
which MS requires service)
An average traffic intensity offered (generated) by each user
Example 1: If a user makes on average two calls per hour, and
that a call lasts an average of 3 minutes
83
Then the total offered traffic intensity for U users are
In a C channel trunked system, if traffic is distributed equally among
channels, then traffic intensity per channel
In Example 1, assume that there are 100 users and 20 channels
Then A = 100(0.1)= 10 and Ac = 10/20 = 0.5
Note: Ac is a measure of the efficiency of channels utilization
Offered traffic is not necessarily the traffic carried by the trunked
system, only that is offered to the system
The maximum possible carried traffic is the total number of
channels, C, in Erlangs84
Example, AMPS system is designed for a GOS of 2% blocking
Channel allocations for cells are designed so that 2 out of 100
calls will be blocked due to channel occupancy during the busiest
hour
What do we do when a call is offered (requested) but all channels
are full?
Blocked calls cleared; Offers no queuing for call requests, Erlang B
Blocked calls delayed, Erlang C
85
Types of trunked systems:
1. Blocked Calls Cleared
No queuing for call requests:
For every user who requests service, it is assumed there is no
setup time and the user is given immediate access to a channel if
channel is available.
If no channels are available, the requesting user is blocked
without access and is free to try again later.
GOS: Erlang B formula determines the probability that a call is
blocked.
86
Erlang B is a measure of the GOS for a trunked system which
provides no queuing for blocked calls
Setting the desired GOS, one can derive
Number of channels needed
The maximum number of users we can support as A = UAU or
The maximum AU we can support (and set the number of
minutes on our calling plans accordingly)
Since C is very high, it is easier to use table or graph form
87
Blocking Probability: Erlang B Formula:
Where C number of trunked channels and A total offered traffic
Assumption to the model
There are infinite number of users.
Call requests are memory less; both new and blocked users may request a
channel at any time.
Service time of a user is exponentially distributed
Traffic requests are described by Poisson model.
Inter-arrival times of call requests are independent and exponentially
distributed.88
89
The Erlang B chart showing the probability of a call being blocked as
a function of the number of channels and traffic intensities in Erlangs
90
2. Blocked Calls Delayed
A queue is provided to hold calls which are blocked.
Instead of clearing a call, put it in a queue and have it wait until a
channel is available
First-in, first-out line; Calls will be processed in the order
received
If a channel is not available immediately, the call request may be
delayed until a channel becomes available.
GOS: Erlang C formula gives the likelihood that a call is
initially denied access to the system
91
There are two things to determine here
The probability a call will be delayed (enter the queue), and
The probability that the delay will be longer than t seconds
The first time is no longer the same as Erlang B
It goes up, because blocked calls aren’t cleared, they “stick
around” and wait for the first open channel
Meaning of GOS
The probability that a call will be forced into the queue AND it
will wait longer than t seconds before being served (for some
given t)
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Additional assumptions:
The queue is infinitely long: Translates to infinite memory
No one who is queued gives up / hangs up (rather than wait)
The probability of an arriving call not having an immediate access
to a channel (or being delayed) is given by Erlang C formula
It is typically easiest to find a result from a chart
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Once it enters the queue, the probability that the delay is greater
than t (for t > 0) is given as
The marginal (overall) probability that a call will be delayed AND
experience a delay greater than t is then
The average delay for all calls in a queued system
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The Erlang C chart showing the probability of a call being delayed as a
function of the number of channels and traffic intensities in Erlangs
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Examples
Consider a system with
• 100 cells• Each cell has C = 20 channels• Generates on average = 2 calls/hour• The average duration of each call (H) = 3 Minutes
How many number of users can be supported if the allowed
probability of blocking is
a . 2% b. 0.2%
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Solution:a. From Erlang B Chart, total carried traffic = 13 Erlangs Traffic intensity per user AU = Hλ = 0.1 Erlangs The total number of users that can be supported by a cell = 13/0.1 =
130 Users/cell Therefore, the total number of users in the system is 13,000
b. Again from Erlang B Chart, total carried traffic = 10 Erlangs Traffic intensity per user AU = Hλ = 0.1 Erlangs The total number of users that can be supported by a cell = 10/0.1 =
100 Users/cell Therefore, the total number of users in the system is 10,000 We support less number of users here
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Summary
Concepts such as handoff, frequency reuse, Trunking efficiency,
and frequency planning are covered
Capacity of cellular system is a function of many things,
E.g., S/I that limits frequency reuse, which intern limits the
number of channels within the coverage area
Trunking efficiency limits the number of users that can access a
trunked radio system.
We may have a block call cleared or block call delayed trunked
system
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