I. Basic Telephonydocshare01.docshare.tips/files/24648/246489525.pdf · TC301 Telecommunication Systems 1-8 Traffic measurements used for long-term network planning are usually based

TC301 Telecommunication Systems

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I. Basic Telephony

Telecommunication deals with the service of providing electrical communication at a distance.

2. Telephone Networks: Introductory Terminology

Telephone network can be regarded as a systematic development of interconnecting transmission media arranged so that one telephone user can talk to any other within that network.

Subscribers share common transmission facilities; switches permit this sharing by concentration. Example: Two towns are separated by 20 miles, and each town has 100

telephone subscribers.

Logically, most of telephone activity (the traffic) will be among the subscribers of the 1st town and among those of the 2nd town.

There will be some traffic, but considerably less from one town to the other.

Let each town has its own switch, perhaps only 6 lines would be required to interconnect the 1st town and the 2nd town.

1. Definition and Concept


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If no more than 6 people want to talk simultaneously between the two towns a number as low as 6 can be selected.

Economics has mandated that we install the minimum number of connecting telephone lines from the 1st town to the 2nd to serve the calling needs between two towns.

The telephone lines connecting one telephone switch or exchange with another are called trunks (in North America) and junctions (in Europe). The telephone lines connecting a subscriber to the switch or exchange that serves the subscriber are called lines, subscriber lines, or loops.

Concentration is a line-to-trunk ratio.

In this example, it was 100 lines to 6 trunks (or junctions) or about a 16:1 ratio. A telephone subscriber looking into the network is served by a local exchange.

This means that the subscriber’s telephone line is connected to the network via the local exchange or central office.

A local exchange has a serving area, which is the geographical area in which the exchange is located; all subscribers in that area are served by that exchange.


3. Essentials of Traffic Engineering

The number of trunks connecting exchange X with exchange Y is the number of voice pairs of their equivalent used in the connection.

One of the most important steps in telecommunication engineering practice is to determine the number of trunks required on a route or connection between exchanges. This is called dimensioning the route. On dimension the route correctly, we need to know the usage which is defined by two parameters:

1. Calling rate: the number of times a route or traffic path is used per unit of time, or more properly defined, “the call intensity per traffic path during the busy hour”.

2. Holding time: the duration of occupancy of a traffic path by a call, or sometimes “the average duration of occupancy of one or more paths by calls.

A traffic path is “ a channel, time slot, frequency band, line , trunk, switch or circuit over which individual communications pass in sequence”.

Carried traffic is the volume of traffic actually carried by a switch.

Offered traffic is the volume of traffic offered to a switch.


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Busy Hour Definition:

1. Busy Hour: refers to the traffic volume or number of call attempts, and is that continuous 1-h period lying wholly in the time interval concerned for which this quantity (i.e., traffic volume or call attempts) is greatest. 2. Peak Busy Hour: the busy hour of each day; it is usually not the same over a number of days. 3. Time Consistent Busy Hour: the 1-h period starting at the same time each day for which the average traffic volume or call-attempt count of the exchange or resource group concerned is greatest over the days under consideration. 4. The Engineering Period (where the Grade of Service criteria is applied) is defined as the busy season busy hour (BSBH), which is the busiest clock hour of the busiest weeks of the year. 5. The Average Busy Season Busy Hour (ABSBH) is used for trunk groups and always has a grade of service criterion applied. For example, for the ABSBH load, a call requiring a circuit in a trunk group should encounter “all trunks busy” (ATB) no more than 1% of the time.


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Figure 1.1 Bar chart of the traffic intensity over a typical working day (United States, mixed business and residence)


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Measurement of Telephone Traffic

If we define telephone traffic as the aggregate of telephone calls over a group of circuits or trunks with regard to the duration of calls as well as their number, the traffic flow (A) is expressed as

Where C denotes the number of calls originated during a period of 1 h and T is the average holding time, usually given in hours.

A is dimensionless unit because we are multiplying calls/hour by hour/call.

Example: Suppose that the average holding time is 2.5 minutes and the

calling rate in the BH for a particular day is 237.

The traffic flow (A) would then be 237 x 2.5 = 592.5 call-minutes (Cm) or

2592.5/60, or about 9.87 call-hours (Ch).

TCA x


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There are another traffic units:

• call-hour (Ch): 1 Ch is the quantity represented by one or more calls having an aggregate duration of 1 h.

• call-second (Cs): 1 Cs is the quantity represented by one or more calls having an aggregate duration of 1 s. Traffic Unit (TU) is a unit of traffic intensity.

One TU is the average intensity in one or more traffic paths carrying an aggregate traffic of 1 Ch in 1 h (the busy hour unless otherwise specified).

I TU = 1 E (Erlang) (numerically)

The equated busy hour call (EBHC) is a European unit of traffic intensity.

One EBHC is the average intensity in one or more traffic paths occupied in the BH by one 2-min call or an aggregate duration of 2 min.

Therefore, we can relate the terms as follows:

1 Erlang = 30 EBHC = 36 CCS* = 60 Cm

Assuming a 1-h time-unit interval.

Note: CCS means “unit call” or “hundred call-second” . This terms express the sum of

number of busy circuits, provided that the busy trunks were observed once every 100 s (36 observations in 1 h).


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Traffic measurements used for long-term network planning are usually based on the traffic in the busy hour (BH), which is usually determined based on observations and studies.

The traditional traffic measurements on trunks during a measurement interval are:

▪ Peg count - calls offered ▪ Usage – traffiic (CCS or Erlangs) carried ▪ Overflow – call encountering all trunks busy

From these measurements, the blocking probability and mean traffic load carried by the trunk group can be calculated. Traffic measurements for short-term management purpose are usually concerned with detecting network congestion.

Calls offered, peg count and overflow count can be used to calculate attempts per circuit per hour (ACH) and connections per circuit per hour (CCH), with these measurements being calculated over very short time periods (e.g., 10-min intervals).


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Under normal circumstances, ACH and CCH are approximately equal. Examples of abnormal conditions are: ▪ ACH high, CCH normal – heavy demand excessive blockage, normal holding times for connected calls indicating that most calls switched are completed, heavy traffic but low congestion. ▪ ACH high, CCH high – heavy traffic, short trunk holding times indicate uncompleted call attempts being switched, congestion.


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Blockage, Lost Calls and Grade of Service

Blockage Scenario: Assume that an isolated telephone exchange serves 5,000

subscribers and that no more than 10% of the subscribers wish service simultaneously.

Therefore, the exchange is dimensioned with sufficient equipment to complete 500 simultaneous connections.

Each connection would be, of course, between any 2 of the 5,000 subscribers.

Now let subscriber 501 attempt to originate a call.

He/She cannot because all the connecting equipment is busy, even though the line he/she wishes to reach may be idle.

This call from subscriber 501 is termed a lost call or blocked call. Grade of Service expresses the probability of meeting blockage during the BH

and is expressed by p.

A typical grade of service is p=0.01 (an average of 1 call in 100 will be blocked

or “lost” during the BH).

Grade of Service, a term in the Erlang formula, is more accurately defined as the probability of blockage.


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Example: If we know that there are 354 seizures (lines connected for service)

and 6 blocked calls (lost calls) during the BH, what is Grade of Service? Or The average Grade of service for a network may be obtained by adding the grade of service contributed by each constituent switch, switching network, or trunk group.

017.0

360

6

6354

6

p

CallsOfferedofNumberTotal

CallsLostofNumberServiceofGrade


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The Reference Data for Radio Engineers states that the Grade of Service provided by a particular group of trunks or circuits of specified size and carrying a specified traffic intensity is the probability that a call offered to the group will find available trunks already occupied on first attempt. That probability depends on a number of factors, the most important of which are:

1. The distribution in time and duration of offered traffic (e.g., random or periodic arrival and constant or exponentially distributed holding time).

2. The number of traffic sources [limited or high (infinite)]

3. The availability of trunks in a group to traffic sources (full or restricted availability)

4. The manner in which lost calls are “handled”.


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Handling of Lost Calls

In conventional telephone traffic theory, three methods are considered for the handling the lost calls:

(1) Lost calls held (LCH): ▪ Assume that the user will immediately reattempt the call on receipt of a congestion signal and will continue to redial. ▪ The user hopes to seize connection equipment or a trunk as soon as switching equipment becomes available for the call to be handled. ▪ This principle is used mainly in North America.

(2) Lost calls cleared (LCC): ▪ Assume that the user will hang up and wait some time interval before reattempting if the user hears the congestion signal on the first attempt. ▪ A Re-attempt (after the delay) is considered as initiating a new call. ▪ The Erlang formula is based on this criterion. ▪ This concept is mainly used in Europe or countries accepting European practice.

(3) Lost calls delayed (LCD): ▪ Assume that the user is automatically put in queue. ▪ It is done in the manual operator or on most modern computer-controlled switching systems. ▪ The waiting calls may be handled LIFO, FIFO or at random.


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Probability-Distribution Curves

Telephone call originations in any particular are random in nature.

The arrival of calls is found fit the Poisson distribution.

Most of common probability-distribution curves are two parameters curves: mean and variance.

The standard deviation s of a sample n observations is

Where is the mean value of

2

1

)(1

1

n

i

i xxn

s

nxxx ,,, 21

nxxx ,,, 21 x

Figure 1.2 A normal distribution curves showing the mean and the standard deviation


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Smooth, Rough and Random Traffic

Coefficient of overdispersion (Variance to Mean Ratio; VMR): : the variance of traffic : the mean of the traffic Traffic probability can be divided into three distinct categories:

• Random: when =1, Poisson distribution is an example of random traffic since VMR=1.

• Rough: when >1, Rough traffic tends to have higher peak than random or smooth traffic. ▪ For a given grade of service, more circuits are required for rough traffic because of the greater spread of the distribution curve (greater dispersion).

• Smooth: when <1, Smooth traffic behaves like random traffic that has been filtered. ▪ The filter is the local exchange, assume that the local exchange has not been over-dimensioned. ▪ The local exchange looking out at its subscribers sees call arrivals as random traffic. ▪ The smooth traffic is the traffic on the local exchange outlets.

2

2


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Smooth traffic is characterized by a Bernoulli distribution.

If we assume that subscribers make calls independently of each other and that

each has a probability p of being engaged in conversation, then if n subscribers

are examined, the probability that x of them will be engaged is

mean =np, variance = np(1-p)

Rough traffic can be characterized by Binomial distribution.

If the distribution parameters are k and q, where k is a positive number

representing a hypothetical number of traffic sources and q represents the

occupancy per source , then

Where R’ is the probability of finding x calls in progress for the parameters k and

q.

Rough traffic is used in dimensioning toll trunks with alternative routing.

xnx ppx

nxB

)1()(

)10( q

kx qqk

kxqkxR )1(

1

1),,(


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Random traffic which is characterized by Poisson distribution can be derived from Binomial distribution.

Assuming that the number of subscribers s is very large and the calling rate

per line h is low such that the product sh=m remains constant and letting s increase to infinity in the limit For most of our discussion, we consider call-holding times to have a negative exponential distribution in the form

Where t/h is the average holding time and P is the probability of a call lasting

longer than t, some arbitrary time interval.

,...2,1,0;!

)( xex

mxP m

x

hteP


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4. Erlang and Poisson Traffic Formulas

When dimensioning a route, we want to find the number of circuits that serve the route. There are several factors to determine the number of circuits (based on the BH traffic load): (1) Call arrivals and holding-time dispersion (2) Number of traffic sources (3) Availability (4) Handling of lost calls

Figure 1.3 Traffic probability distributions: smooth, random and rough traffic.


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The Erlang B loss formula has been widely used today.

The probability of blockage at the switch due to congestion is expressed as grade

of service (EB) or the probability of finding x channels busy.

Where n is the number of trunks or servicing channels,

A is the mean of the offered traffic,

EB is the grade of service using the Erlang B formula.

This formula assumes the following:

▪ Traffic originates from an infinite number of sources.

▪ Lost calls are cleared assuming a zero holding time.

▪ The number of trunks or servicing channels is limited.

▪ Full availability exists.

!!21

!2 nAAA

nAE

n

n

B


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Alternative Traffic Formula Conventions

Let A = the expected traffic density, expressed in busy hour Erlangs.

P = The probability that calls will be lost (or delayed) because of insufficient

channels.

n = the number of channels in the group of channels.

s = the number of sources in the group of sources.

p = the probability that a single source will be busy at an instant of

observation. This is equal to A/s.

x = A variable representing a number of busy sources or busy channels.

e = the Neperian logarithmic base, which is the constant 2.71828+.

= the combination of m things taken n at a time.

= the summation of all values obtained when each integer or whole

number value, from m to n inclusive, is substituted for the value x in the

expression following the symbol. = the conventional symbol for infinity.

n

m

n

mX


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The Poisson formula: Under the following assumptions: • Infinite sources • Equal traffic density per source • Lost calls held (LCH)

The Erlang B formula: Under the following assumptions: • Infinite sources • Equal traffic density per source • Lost calls cleared (LCC)

nx

xA

x

AeP

!

n

x

x

n

xA

nAP

0

!

!


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The Erlang C formula: Under the following assumptions: • Infinite sources • Lost calls delayed (LCD) • exponential holding times • Calls served in order of arrival

The Binomial formula: Under the following assumptions: • Finite sources • Equal traffic density per source • Lost calls held (LCH)

An

n

n

A

x

A

An

n

n

A

Pnn

x

x

n

!!

!1

0

111s

nx

xs

As

A

x

s

s

AsP


From Erlang Table, we can find the total capacity in Erlangs for the 0.5% GoS from different numbers of channels.

By using the relation , where U is the number of users and Au is the

traffic per user, we can obtain the total number of users that can be supported in the system.

(a) Given C=1, Au =0.1, GoS=0.005, from Fig.2.2.1(a), we obtain A=0.005.

Therefore, total number of users, U=A/Au = 0.005/0.1 = 0.05 users.

But actually one user could be supported on one channel, so U=1.

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Example 4.1.1: How many users can be supported for a 0.5% blocking

probability for the following number of trunked channels (C) in a blocked calls

system?

(a)1, (b) 5, (c) 10, (d) 20, (e) 100.

Assume each user generates 0.1 Erlangs for traffic.

uUAA

Solution:


(b) Given C=5, Au =0.1, GoS=0.005, from Erlang Table, we obtain A=1.132.

Therefore, total number of users, U=A/Au = 1.132/0.1 = 11 users.

(c) Given C=10, Au =0.1, GoS=0.005, from Erlang Table, we obtain A=3.961.


(d) Given C=20, Au =0.1, GoS=0.005, from Erlang Table, we obtain A=11.09.


(e) Given C=100, Au =0.1, GoS=0.005, from Erlang Table, we obtain A=80.91.


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Solution: (cont.)


25

Example 4.1.2: An urban area has a population of two million residents.

Three competing trunked mobile networks (systems A, B and C) provide cellular service in this area.

System A has 394 cells with 19 channels each,

system B has 98 cells with 57 channels each, and

system C has 49 cells, each with 100 channels.

Find the number of users that can be supported at 2% blocking if each user averages two calls per hour at an average call duration of 3 minutes.

Assuming that all 3 trunked systems are operated at maximum capacity, compute the percentage market penetration of each cellular provider.


System A Given : Probability of blocking = 2% =0.02

Number of channels per cell used in the system, C=19

Traffic intensity per user, Erlangs, where is the average call rate and H is the average call duration.

For GoS =0.02, and C = 19, from the Erlang B chart,

the total carried traffic, A, is obtained as 12.33 Erlangs.

Therefore, the number of users that can be supported per cell is

U=A/Au =12.33/0.1 = 123.

Since there are 394 cells, the total number of subscribers that can be supported by system A is equal to 123 x 394 = 48,462.

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Solution:

1.0)60/3(2 xHAu


System B Given : Probability of blocking = 2% =0.02


Traffic intensity per user, Erlangs




U=A/Au =46.82/0.1 = 468.

Since there are 98 cells, the total number of subscribers that can be supported by system B is equal to 468 x 98 = 45,864.

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Solution: (cont.)

1.0)60/3(2 xHAu


System C Given : Probability of blocking = 2% =0.02


Traffic intensity per user, Erlangs




U=A/Au =87.97/0.1 = 879.

Since there are 49 cells, the total number of subscribers that can be supported by system C is equal to 879 x 49 = 43,071.

Therefore, total number of cellular subscribers that can be supported by these three systems are 48,462+45,864+43,071 = 137,397 users.

Since there are 2 million residents in the given urban area, System A’s market penetration = 48,462/2,000,000 = 2.42% System B’s market penetration = 45,864/2,000,000 = 2.29% System C’s market penetration = 43,071/2,000,000 = 2.15% Total market penetration of the three systems = 6.87%

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Solution: (cont.)

1.0)60/3(2 xHAu


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Example 4.1.3: A Hexagonal cell within 4-cell system has a radius of 1.387 km.

A total of 60 channels are used within the entire system.

If the load per user is 0.029 Erlangs, and call/hour,

compute the following for an Erlang C system that has a 5% probability of a delayed call:

(a) How many users per square kilometer will this system support?

Given that the area covered per cell is where R is the radius of a cell.

1

25981.2 R


Given: Cell radius, R=1.387 km,

Area covered per cell is sq.km. Number of cells per cluster = 4 Total number of channels = 60 Therefore, number of channels per cell = 60/4 = 15 channels.

From Erlang C chart, for 5% probability of delay with C= 15,

traffic intensity = 9.044 Erlangs. Therefore, number of users = total traffic intensity/traffic per user = 9.044/0.029 = 311 users =311 users/5 sq.km = 62 users/sq.km

30

Solution:

5)387.1(5981.2 2 x


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5. Queuing Systems-Server-Pool Traffic

Server pools are groups of traffic sources, such as signaling registers and operator positions, that are used on a shared basis.

Service requests that cannot be satisfied immediately are placed in a queue and served on a first-in, first-out (FIFO) basis.

Server-pool traffic is directly related to offered traffic, server holding time and call-attempt factor and is inversely related to call-holding time.

This is expressed as follows:

Where AS = server-pool traffic in Erlangs

AT = total traffic served in Erlangs

TS = mean server-holding time in hours

TC = mean call-holding time in hours

C = call-attempt factor (dimensionless)

C

STS

T

CTAA

..


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Total traffic served refers to the total offered traffic that requires the services of the specific server pool for some portion of the call.

For example, a dual-tone multi-frequency (DTMF) receiver pool is dimensioned to serve only the DTMF tone-dialing portion of total switch traffic generated by DTMF signaling resources. The mean server-holding time is the arithmetic average of all server-holding times for the specific server pool.

We can calculate mean server-holding time for calls with different holding-time characteristics using the following equation:

Where TS = mean server-holding time in hours

T1, T2, …, Tn = individual server-holding times in hours

a, b, …, k = fractions of total traffic served (a+b+…+k=1)

nS TkTbTaT ... 21


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Example: Determine the mean DTMF receiving-holding time for a switch

where subscribers dial local calls using a 7-digit number and long-distance calls using an 11-digit number. Assume that 70% of the calls are local calls, the remainder are long-distance calls, and the typical signaling register holding times found in the following table is applicable.

Number Of digits Received Or Sent

Signal register 1 4 7 10 11

Local dial-pulse (DP) receiver 3.7 8.3 12.8 17.6 19.1

Local DTMF receiver 2.3 5.2 8.1 11.0 12.0

Incoming MF receiver 1.0 1.4 1.8 2.2 2.3

Outgoing MF sender 1.5 1.9 2.3 2.8 3.0

sssTS 27.9)0.12)(3.0()1.8)(7.0(


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Call-attempt factors are dimensionless numbers that adjust offered traffic intensity to compensate for call attempts that do not result in complete calls.

Therefore, call-attempt factors are inversely proportional to the fraction of completed calls as defined in the following equation:

Where C = call-attempt factor (dimensionless)

k = fraction of calls completed (decimal fraction)

kC 1

Call-attempt Disposition Percentage

Call was completed 70.7

Call subscriber did not answer 12.7

Called subscriber line was busy 10.1

Call abandoned without system response 2.6

Equipment blockage or failure 1.9

Customer dialing error 1.6

Called directory number changed or disconnected 0.4

Example: Determine the

call-attempt factors for these data, where 70% of the calls were completed

(k =0.707)

414.1707.0

11

kC


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6. Dimensioning and Efficiency

One method of improving efficiency is to use alternative routing.

Simplified diagram of the alternative routing concept (solid line represents direct route, dashed line represents alternative route carrying the overflow from X to Y ).


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Traffic peakiness, the peaks representing overflow onto alternative routes

Here, the overflow traffic is the “lost” traffic in the Erlang B calculations.

Let M be the mean value of that overflow and A be the random traffic offered

to a group of n circuits (trunks). Then

When the overflow traffic from several sources is combined and offered to a single 2nd (or 3rd, 4th , etc.) choice of a group of circuits, both the mean and the variance of the combined traffic are the arithmetic sums of the means and variances of the contributors.

AMn

AMMV

11


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7. Bases of Network Configurations

Subscribers access the network by a nearby local exchange.

There are 3 basic methods of connection in conventional telephony:

(a) Mesh: used when there are comparatively high traffic levels between exchanges, such as metropolitan networks.

(b) Star: be applied when traffic level is comparatively low.

(c) Double and high-order star. In practice, most networks are compromises between mesh and star configurations.


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A typical telephone network serving a small city as an example of a compromise between mesh and star configuration. A is the highest level in this simple hierarchy.

A might house the ‘‘point of presence’’ (POP) in the U.S. network. B is a local exchange.

C may be a satellite exchange or a concentrator.


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We illustrate the order of importance of the several levels in a high-order star network.

There are 3 levels of exchanges.

There are restrictions or rules of traffic flow: - Traffic from 3A1 to 3A2 would have to flow through exchange 2A1. - Likewise, traffic from exchange 2A2 to 2A3 would have to flow through exchange 1A.


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8. Quality of Service

Quality of Service appears at the outset to be an intangible concept. Quality of service also means how happy the telephone company (or other common carrier) is keeping the customer. Quality of Service in telephone system can be

• Delay before receiving dial tone (“dial-tone delay”)

• Postdial(ing) delay (time from completion of dialing a number to first ring of telephone called).

• Availability of service tones (busy tone, telephone out of order, etc.)

• Correctness of billing

• Reasonable cost to customer of service

• Responsiveness to servicing requests

• Responsiveness and courtesy of operators

• Time to installation of new telephone and by some, the additional services offered by the telephone company.

Documents

I. Basic Telephonydocshare01.docshare.tips/files/24648/246489525.pdf · TC301 Telecommunication Systems 1-8 Traffic measurements used for long-term network planning are usually based