Lecture 3

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Trunking and Grade of Service• Cellular radio systems rely on trunking to accommodate a

large number of users in a limited radio spectrum.

• Trunking system– A mechanism to allow many users 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.2

Trunking• Trunking exploits the statistical behavior of users so that a fixed

number of channels may accommodate a large random user community

• There is a trade-off between the number of available telephone circuits and the likelihood of a particular user finding that no circuits are available during the peak calling times

• As the number of phone lines decreases, it becomes more likely that all circuits will be busy for a particular user

• In a trunked mobile radio system, when a particular user requests service and all of the radio channels are already in use, the users is blocked or denied access to the system. In some systems a queue may be used to hold requesting users until a channel becomes available

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Erlang• The fundamentals of truncking theory were developed by Erlang, a

Danish mathematician who, in the late 19th century embarked on the study of how a large population could be accommodated by a limited number of servers.

• Erlang: a “dimensionless unit,” – The basic unit of telecom traffic intensity carried a channel that is

completely occupied (one call-hour/hour or one call-min/min)• Since a single circuit used continuously carries 60 minutes of calling

in one hour, one Erlang is usually defined as 60 minutes of traffic• A radio channel that is occupied for 30 minutes during an hour carries

0.5 Erlangs of traffic

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Grade of Service

GOS is a benchmark used to define the desired performance of a particular trunked system

• Grade of Service (GOS): probability that a call is blocked (or delayed).

• The probability that all servers will be busy when a call attempt is made. For example, on a trunk group: GOS of 2% means that there is a 2% probability of getting a busy signal (being “blocked”) when you have a given amount of traffic and a given number of trunks.

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Grade of Service

• It is a wireless designer’s job to estimate the maximum required capacity and to allocate the proper number of channels in order to meet GOS

• AMPS is designed for GoS of 2% blocking. This means that channel allocations for cell sites are designed so that 2 out of 100 calls will be blocked due to channel occupancy during the busiest hour

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Common Terms of Trunking Theory

• Set-up Time: The time required to allocate a trunked radio channel to a requesting user

• Blocked Call: Call which cannot be completed at time of request, due to congestion. (lost call)

• Holding Time: Average duration of a typical call. Denoted by H (in hours)

• Traffic Intensity: Measure of channel time utilization, which is the channel occupancy measured in Erlangs. Denoted by A

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• The traffic intensity offered by each user is equal to the call request rate multiplied by the holding time. Each user generates a traffic intensity of

• Au Erlangs given by

• H is the average duration of a call• λ =avg No. of call requests per unit time for each

user

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• For a system containing “U” users and an unspecified No. of channels,

• Total offered traffic Intensity=A=UAu

• In a “C” channel trunked system, if the traffic is equally distributed among the channels, traffic intensity per channel, Ac = UAu / C

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Important!• Offered traffic is not necessarily the traffic which

is carried by the trunked system• It is only that which is offered to the trunk system• When the offered traffic exceeds the maximum

capacity of the system, the carried traffic becomes limited due to the limited availability of the No. of channels

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Block Calls cleared/Erlang B System

• In Erlang B System, a call request is simply denied if all channels in the pool are in use

• Assumptions– Any user can require a channel any time– Probability of user occupying a channel is exponential– Finite trunk channels available

– No queuing, for call requests if no channels are available, requesting user is blocked

– it is assumed that there is no setup time and user is given immediate access to a channel if one is available

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Probability of Blocking• The GOS measure for Block Calls Cleared System

is the probability that a user’s call request is blocked

• The Erlang B formula determines the blocking probability, p, given a certain total offered traffic intensity, A, and a certain number of channels C in the pool

• A is the total offered traffic• Since some calls are blocked, A is not the traffic

carried by the system

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Erlang-B Formula

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Capacity of Erlang B System

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Erlang B Chart

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Blocked Calls delayed/Erlang C• A queue is provided to hold calls which are blocked• If a channel is not available immediately, the call request may be

delayed until a channel becomes available

• Its measure of GOS is defined as the probability that a call is blocked after waiting a specific length of time in the queue

• To find the GOS, it is first necessary to find the likelihood that a call is initially denied access to the system

• This likelihood of a call not having immediate access to a channel is determined by Erlang C formula

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Erlang-C Formula

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Erlang C Chart

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Example

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Example

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Example

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Example

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Example

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ConclusionTrunking efficiency is a measure of • No of users which can be offered a particular GOS with a particular

configuration of fixed channels• Way in which channels are grouped substantially alters the number of

users handled by a trunked system • 10 trunked channels at a GOS of 0.01 can support 4.46 Erlangs of

traffic • But two groups of 5 trunked channels can support 2 × 1.36 Erlangs, or

2.72 Erlangs of traffic• 10 channels trunked together support 60% more traffic at a specific

GOS than do two five channel trunks! • So allocation of channels in a trunked radio system has a major impact

on overall system capacityDo look at remaining examples!

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Assignment

• Pr 3.4, 3.5, 3.10, 3.11, 3.13, 3.15, 3.28

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Nearest co-channel NeighborStep 1:

Move “i” cells along any chain of hexagons

Step 2:

Turn 60o counter clockwise and move “j” cells

i=3, j=2

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Prove N=i2+j2+ij Let radius of each cell = R Let distance b/w center and center of one side of hexagon = r Let distance b/w centers of Co-channel Cells = D O

C 2

ROC

O

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Hexagonal Cluster

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Hexagonal Cluster

• Each cluster is surrounded by 6 similar clusters with the same orientation

• Each cluster has a total area equivalent to what can be called a “super-hexagon”

• view a cluster as a “hexagon”

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Cluster Size

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Co-Channel Reuse Ratio

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