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

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Lecture Outlines

Introduction

Cellular Concept & Frequency Reuse

Channel Assignment Strategies

Handoff Strategies

Interference and System Capacity

Trunking and Grade of Services

Summary

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Used Acronyms • BS: Base station • MS: Mobile station • MSC: Mobile switching center • GOS: Grade of services • CCI : Co-channel interference • ACI: Adjacent channel interference

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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

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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

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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

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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

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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

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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

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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

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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

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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, …

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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

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Example : N=7, i=2,j=1

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Example : N=28, i=4, j=2

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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

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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

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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,...

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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

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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

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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

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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

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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.

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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

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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.

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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

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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.

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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

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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.

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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

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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.

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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

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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

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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

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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

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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.

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This concept minimizes the number of handoffs for high speed

users and provides additional micro cell channels for pedestrian

users

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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

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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

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Co-channel reuse ratio for some values of N

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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

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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)

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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

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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

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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.

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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.

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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.

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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.

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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

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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.

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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 .

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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.

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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).

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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.

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Computation of GOS

Analysis

Average arrival rate(λ): Average number of MSs requesting

service (call request/time)

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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

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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

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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.

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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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